Emma and Lily jog in the same direction along a straight track. For 0≤t≤15, Emma’s velocity at time t is given by E(t)=7510t2−7t+80.22 and Lily’s velocity at time t is given by L(t)=12t3e−0.5t. Both E(t) and L(t) are positive for 0≤t≤15 and are measured in meters per minute, and t is measured in minutes. Emma is 10 meters ahead of Lily at time t=0, and Emma remains ahead of Lily for 0
Answers
Answer:
a) 103.176 m / min
b) 1751.28 meters
Explanation:
Given:-
- Emma's and Lily's velocities ( E(t) and L(t) ) are given as functions respectively:
\(E(t) = \frac{7510}{t^2-7t + 80.22} \\\\L ( t ) = 12t^3*e^-^0^.^5^t\)
- Where, E ( t ) and L ( t ) are given in m / min
- Both run for a total time of 15 minutes in the same direction along the straight track defined by the absolute interval:
( 0 ≤ t ≤ 15 ) mins
- It is known that Emma is 10 meters ahead of Lily at time t = 0.
Find:-
a) Find the value of \(\frac{1}{6}*\int\limits^8_2 {E(t)} \, dt\) using correct units, interpret the meaning of
b) What is the maximum distance between Emma and Lily over the time interval 0 ≤ t ≤ 15?
Solution:-
- The average value of a function f ( x ) over an interval [ a , b ] is determined using calculus via the following relation:
\(f_a_v_g = \frac{1}{b-a}\int\limits^a_b {f(x)} \, dx\)
- The first part of the question is asking us to determine the average velocity of Emma over the time interval of ( 2 , 8 ). Therefore, ( E_avg ) can be determined using the above relation:
\(E_a_v_g = \frac{1}{8 - 2}*\int\limits^8_2 {E(t)} \, dt\\\\E_a_v_g = \frac{1}{6}*\int\limits^8_2 {E(t)} \, dt\\\)
- We will evaluate the integral formulation above to determine Emma's average velocity over the 2 ≤ t ≤ 8 minute range:
\(E_a_v_g = \frac{1}{6}*\int\limits^8_2 {\frac{7510}{t^2 - 7t + 80.22} } \, dt\\\\E_a_v_g = \frac{1}{6}*37550\int\limits^8_2 {\frac{1}{50t^2 - 350t + 4011} } \, dt\\\\\)
- Complete the square in the denominator:
\(E_a_v_g = \frac{1}{6}*37550\int\limits^8_2 {\frac{1}{(5\sqrt{2}*t - \frac{35}{\sqrt{2} })^2 + \frac{6797}{2} } } \, dt\\\\\)
- Use the following substitution:
\(u = \frac{5*(2t - 7 )}{\sqrt{6797} } \\\\\frac{du}{dt} = \frac{10}{\sqrt{6797} } \\\\dt = \frac{\sqrt{6797}}{10}.du\)
- Substitute the relations for (u) and (dt) in the above E_avg expression.
\(E_a_v_g = \frac{1}{6}*37550\int {\frac{\sqrt{6797} }{5*(6797u^2 + 67997) } } \, du\\\\E_a_v_g = \frac{1}{6}*37550*\frac{1}{5\sqrt{6797}} \int {\frac{1 }{(u^2 + 1) } } \, du\)
- Use the following standard integral:
\(arctan(u) = \int {\frac{1}{u^2 + 1} } \, du\)
- Evaluate:
\(E_a_v_g = \frac{1}{6}*37550*\frac{1}{5\sqrt{6797}}* arctan ( u ) |\)
- Apply back substitution for ( u ):
\(E_a_v_g = \frac{1}{6}*[\frac{75100* arctan ( \frac{5*(16 - 7 )}{\sqrt{6797} } )}{\sqrt{6797} } - \frac{75100* arctan ( \frac{5*(4 - 7 )}{\sqrt{6797} } )}{\sqrt{6797} } ]\\\\\)
- Plug in the limits and find Emma's average velocity:
\(E_a_v_g = 151.82037*[arctan (0.54582 ) - arctan ( -0.18194 ) ]\\\\E_a_v_g = 103.176 \frac{m}{min}\)
Answer: Emma's average speed over the interval ( 2 ≤ t ≤ 8 ) is 103.179 meters per minute.
- The displacement S ( E ) of Emma from time t = 0 till time ( t ) over the absolute interval of 0≤t≤15 is given by the relation:
\(S (E) = S_o + \int\limits^t_0 {E(t)} \, dt\\\\S ( E ) = 10 + \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } |_0^t\\\\S ( E ) = 10 + [ \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } - \frac{75100*arctan( \frac{5*(0 - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } ]\\\\S ( E ) = \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } + 375.71098\\\)
- The displacement S ( L ) of Lily from time t = 0 till time ( t ) over the absolute interval of 0 ≤ t ≤ 15 is given by the relation:
\(S (L) = \int\limits^t_0 {L(t)} \, dt\\\\S (L) = \int\limits^t_0 ({12t^3 *e^-^0^.^5^t } )\, .dt\\\)
Apply integration by parts:
\(S ( L ) = 24t^3*e^-^0^.^5^t - 64*\int\limits^t_0 ({e^-^0^.^5^t*t^2} \,) dt\\\)
Re-apply integration by parts 2 more times:
\(S ( L ) = -24t^3*e^-^0^.^5^t + 64*[ -2t^2*e^-^0^.^5^t - 2\int\limits^t_0 ({e^-^0^.^5^t*t} \,) dt ]\\\) \(S ( L ) = -24t^3*e^-^0^.^5^t + 64*[ -2t^2*e^-^0^.^5^t - 2*( -2t*e^-^0^.^5^t - (4e^-^0^.^5^t - 4 ) ]\\\\\)
\(S ( L ) = e^-^0^.^5^t* ( -24t^3 -128t^2+ 256t + 512) - 512 \\\)
- The distance between Emma and Lily over the time interval 0 < t < 15 mins can be determined by subtracting S ( L ) from S ( E ):
\(S = S ( E ) - S ( L )\\\\S = \frac{75100*arctan( \frac{5*(2t - 7 )}{\sqrt{6797} }) }{\sqrt{6797} } - e^-^0^.^5^t* ( -24t^3 -128t^2+ 256t + 512) + 887.71098\\\)
- The maximum distance ( S ) between Emma and Lily is governed by the critical value of S ( t ) for which function takes either a minima or maxima.
- To determine the critical values of the function S ( t ) we will take the first derivative of the function S with respect to t and set it to zero:
\(\frac{dS}{dt} = \frac{d [ S(E) - S(L)]}{dt} \\\\\frac{dS}{dt} = E(t) - L(t) \\\\\frac{dS}{dt} = \frac{7510}{t^2 - 7t+80.22} - 12t^3*e^-^0^.^5^t = 0\\\\( 12t^5 - 84t^4 + 962.64t^3) *e^-^0^.^5^t - 7510 = 0\\\\t = 4.233 , 11.671\)
- We will plug in each value of t and evaluate the displacement function S(t) for each critical value:
Related Questions
Paola conducts an investigation to determine how temperature affects plant growth. Each plant started at the same height, received the same amount of water and was planted in the same type of soil She
recorded her results every seven days for three weeks.
Pls help
Answers
Answer:
HE IS WON
Explanation:
JESUS
Super fine 40-gauge copper wire has a diameter of only and weighs only . Suppose a spool of 40-gauge wire weighs less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used
Answers
This question is incomplete, the complete question is;
Super fine 40-gauge copper wire has a diameter of only 0.080 mm and weighs only 44.5 g/km. Suppose a spool of 40-gauge wire weighs 205 g less after some wire is pulled off to wind a magnet. How could you calculate how much wire was used ?
Answer: length of wire to be used is 4.6067 km
Explanation:
Circular diameter = d mm
Linear mass density of wire = μ g/km
let m be the mass of wire un-winded from spool to wind a magnet.
If M is mass of wire initially
then
Δm = M - m { which represents decrease of mass }
Also if L rep the length of wire pulled off,
then
Δm = μ × L grams
⇒ L = Δm/μ km
now given that weight Δm = 205 g and length per unit weight μ = 44.5 g/km
we substitute
L = 205 g / 44.5 g/km
L = 4.6067 km
Therefore length of wire to be used is 4.6067 km
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
Answers
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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You are designing a machine for a space exploration vehicle. It contains an enclosed column of oil that is 1.50 m tall, and you need the pressure difference between the top and the bottom of this column to be 0.125 atm. (a) What must be the density of the oil? (b) If the vehicle is taken to Mars, where the acceleration due to gravity is 0.379g, what will be the pressure difference (in earth atmospheres) between the top and bottom of the oil column?
Answers
Answer:
Explanation:
(a) To find the density of the oil, we can use the formula for pressure difference in a fluid column:
ΔP = ρgh
where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
Plugging in the given values, we have:
0.125 atm = ρgh = ρ(9.81 m/s^2)(1.50 m)
Solving for ρ, we get:
ρ = 0.125 atm / (9.81 m/s^2 x 1.50 m) ≈ 0.00847 g/cm^3
Therefore, the density of the oil must be approximately 0.00847 g/cm^3.
(b) On Mars, the acceleration due to gravity is 0.379 times that of Earth, or g_Mars = 0.379g_Earth. The pressure difference between the top and bottom of the oil column will be:
ΔP_Mars = ρgh_Mars = ρg_Earth(0.379)(1.50 m)
Using the density we found in part (a), we have:
ΔP_Mars = (0.00847 g/cm^3)(9.81 m/s^2)(0.379)(1.50 m) / (1 atm/101325 Pa)
ΔP_Mars ≈ 0.019 atm
So, the pressure difference between the top and bottom of the oil column on Mars will be approximately 0.019 atm, or about 0.15 times the pressure difference on Earth.
Answer:
The pressure difference (in Earth's atmosphere) between the top and bottom of the oil column on Mars is 0.045 atm.
Explanation:
(a) To find the density of the oil, we can use the formula for pressure difference in a fluid column: ΔP = ρgh, where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
We know that the pressure difference is 0.125 atm, the height of the column is 1.50 m, and the acceleration due to gravity on Earth is 9.81 m/s². Plugging in these values, we get:
0.125 atm = ρ(9.81 m/s²)(1.50 m)
Solving for ρ, we get:
ρ = 0.00803 g/cm³
Therefore, the density of the oil must be 0.00803 g/cm³.
(b) If the vehicle is taken to Mars, where the acceleration due to gravity is 0.379g, we can use the same formula to find the pressure difference:
ΔP = ρgh
We know that the height of the column is still 1.50 m, but the acceleration due to gravity is now 0.379g. Plugging in these values, we get:
ΔP = (0.00803 g/cm³)(9.81 m/s²)(0.379)(150 cm)
Solving for ΔP, we get:
ΔP = 0.045 atm
Therefore, the pressure difference (in Earth's atmosphere) between the top and bottom of the oil column on Mars is 0.045 atm.
De que esta hecho el sol? plisss ayuda.no necesito un texto de 100 reglones, puede ser resumido en solo 2 renglones
Answers
A 100V battery connected to two oppositely charged plates that are 10cm apart.
a. What is the magnitude of the electric field?
b. What is the electric force exerted on a +200uC ?
Answers
Answer:
Work to move unit charge from one plate to the other separated by d
W = E q d
Electric potential: V = W / q
E = V / d = 100 Volts / .1 m = 1000 Volts / m
F = E q = 1000 Joule / C m * 2 * 10E-4 C
F = .2 J / m = .2 N
What causes wind? A. differences in land elevation on a continent B. the angle at which the rays from the sun hit the atmosphere C. air flowing from a high pressure area to a low pressure area D. gravity pull caused by the moon moving farther away from the earth
Answers
Answer:
C
Explanation:
I think it C because I learnt about it in geography and my teacher approves. Maybe
example of wood wind musical instrument
Answers
Flute, Clarinet, Saxophone, Piccolo, Tenor Sax oboe
Piccolo
Flute
Clarinet
Saxophone (all registers)
Oboe
English Horn
Bassoon
b(4+a) ;where a = 6 and b - 2
Answers
= 2(4+6)
= 2×10
= 20
HOPE IT HELPS !!!!!!!!
MARK AS BRAINLIEST
To accelerate, an object must
Answers
Answer:
be acted upon an object or person
Explanation:
a force in the opposite direction
of the motion
Answers
forces: forces applied to an object in opposite directions that are not equal in size. Unbalanced forces result in a change in motion. friction: the force that opposes the motion or tendency toward motion of two objects that are in contact.
a boy throws a ball horizontally from shoulder height of 1.10m just before the ball touches down on the level ground it makes an angle of 30 degree with the ground. determine the initial velocity of the ball as it left the boys hand
Answers
The boy throws the ball horizontally. The initial velocity of the ball as it left the boy's hand was approximately 3.72 m/s.
What is initial velocity?Initial velocity, often represented as v0, is the velocity of an object at the beginning of a time interval or at the start of a motion.
Use the following kinematic equations to arrive at the answer:
Horizontal velocity (Vx) = Distance / Time
Vertical displacement (y) = V0y*t + (1/2)gt²
Vertical velocity (Vy) = V0y + g*t
Tan(theta) = Vy / Vx
where V0y is the initial vertical velocity, g is acceleration due to gravity (9.8 m/s²), and theta is the angle of inclination.
First, let's find the time it takes for the ball to hit the ground. We can use the vertical displacement equation and set y = 0:
0 = V0y*t + (1/2)gt²
Simplifying and solving for t, we get:
t = sqrt((2y) / g)
= sqrt((21.10 m) / 9.8 m/s²)
= 0.472 s
Now, we can use the horizontal velocity equation to find Vx. Since the ball was thrown horizontally, Vx is the same as the initial velocity (V0):
Vx = Distance / Time
= (horizontal distance travelled by ball) / t
We don't know the horizontal distance travelled by the ball, but we can find it using the vertical displacement equation. At the instant the ball hits the ground, its vertical displacement (y) is:
y = V0y*t + (1/2)gt²
= 0 + (1/2)gt²
= (1/2)*9.8 m/s² * (0.472 s)²
= 1.10 m
This means the ball travelled a total distance of:
distance = horizontal distance + vertical distance
= x + 1.10 m
where x is the horizontal distance travelled by the ball. We can find x using the angle of inclination and the vertical displacement:
Tan(theta) = Vy / Vx
Vy = V0y + g*t
Solving for V0y, we get:
V0y = Vy - g*t
Plugging in the numbers, we get:
V0y = Tan(theta) * Vx - g*t
= Tan(30 deg) * Vx - 9.8 m/s² * 0.472 s
= 0.577 * Vx - 4.62 m/s
Now, we can use the vertical displacement equation again to find x:
y = V0yt + (1/2)gt²
= (0.577Vx - 4.62 m/s) * 0.472 s + (1/2)*9.8 m/s² * (0.472 s)²
= 1.10 m
Simplifying and solving for Vx, we get:
Vx = (2y - 0.577V0t) / t
= (21.10 m - 0.577*(0.577*Vx - 4.62 m/s)*0.472 s) / 0.472 s
= 3.72 m/s
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A rocket has a mass of 156,789 kg and is traveling at 45.6 m/s. How much kinetic energy does the rocket
possess?
Answers
Explanation:
K.E =1/2 mv^2
=1/2(156789)(45.6)^2
=78,394.5 × 2,079.36
=163,010,387.52 kg m/s
This should be your answer.
A circular loop of wire has radius of 9.50 cmcm. A sinusoidal electromagnetic plane wave traveling in air passes through the loop, with the direction of the magnetic field of the wave perpendicular to the plane of the loop. The intensity of the wave at the location of the loop is 0.0215 W/m2W/m2, and the wavelength of the wave is 6.90 mm.What is the maximum emf induced in the loop?
Express your answer with the appropriate units.
Answers
Answer:
The induced emf is \(\epsilon = 0.1041 \ V\)
Explanation:
From the question we are told that
The radius of the circular loop is \(r = 9.50 \ cm = 0.095 \ m\)
The intensity of the wave is \(I = 0.0215 \ W/m^2\)
The wavelength is \(\lambda = 6.90\ m\)
Generally the intensity is mathematically represented as
\(I = \frac{ c * B^2 }{ 2 * \mu_o }\)
Here \(\mu_o\) is the permeability of free space with value
\(\mu_o = 4 \pi *10^{-7} N/A^2\)
B is the magnetic field which can be mathematically represented from the equation as
\(B = \sqrt{ \frac{ 2 * \mu_o * I }{ c} }\)
substituting values
\(B = \sqrt{ \frac{ 2 * 4\pi *10^{-7} * 0.0215 }{ 3.0*10^{8}} }\)
\(B = 1.342 *10^{-8} \ T\)
The area is mathematically represented as
\(A = \pi r^2\)
substituting values
\(A = 3.142 * (0.095)^2\)
\(A = 0.0284\)
The angular velocity is mathematically represented as
\(w = 2 * \pi * \frac{c}{\lambda }\)
substituting values
\(w = 2 * 3.142 * \frac{3.0*10^{8}}{ 6.90 }\)
\(w = 2.732 *10^{8} rad \ s^{-1}\)
Generally the induced emf is mathematically represented as
\(\epsilon = N * B * A * w * sin (wt )\)
At maximum induced emf \(sin (wt) = 1\)
So
\(\epsilon = N * B * A * w\)
substituting values
\(\epsilon = 1 * 1.342 *10^{-8} * 0.0284 *2.732 *10^{8}\)
\(\epsilon = 0.1041 \ V\)
Describe the differences between a HALL effect sensor and a permanent magnet sensor. Which one is more accurate?
Answers
The difference is that Hall effect sensor detects the strength of a magnetic field perpendicular to it, while a permanent magnetic sensor detects the angle of a parallel magnetic field.
The permanent magnetic sensor tends to be more accurate as it has a bigger detectable area that has detects layout error.
What is a magnet?
A magnet is any material that produces a magnetic field. A magnet has north and south poles at opposite ends.
The difference between a hall effect magnet and a permanent magnet sensor is that hall effect detects magnetics fields perpendicular to it while a permanent magnet detects magnetic fields parallel to it.
In conclusion, the permanent magnet is more accurate as it has a wider detectable area.
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I NEED HELP THIS QUESTION IS SO HARDDD!!
Answers
Answer:
c
Explanation:
search it up
Answer:
Option A.
Explanation:
Because this is a lunar eclipse it normally happens 2 times a year. This is a decently rare phenomenon due to the positions they have to be in to make a lunar eclipse. Therefore, it is option A.
What is the coefficient of LiCl when the below double replacement reaction is balanced?
LiCl + BeF2 → LiF + BeCl2
2
O4
Answers
Answer:2
Explanation:
What is the charge of the particle on an aluminum rod with a 0.946 that you pass between the poles of a 0.41-T permanent magnet at a speed of 4.05 m/s at a 90o angle?
Answers
The charge of the particle on the aluminum rod is 9.26 x 10^-6 C.
When a charged particle moves through a magnetic field, it experiences a force known as the Lorentz force. The Lorentz force is given by the equation F = qvBsinθ, where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.
In this scenario, an aluminum rod with a mass of 0.946 g is passed between the poles of a 0.41-T permanent magnet at a speed of 4.05 m/s at a 90o angle. Since aluminum is a conductor, it is expected that electrons in the metal will be free to move, allowing for a current to flow through the rod.
We can calculate the charge of the particle by using the equation F = ma, where F is the Lorentz force, m is the mass of the particle, and a is the acceleration of the particle.
The acceleration of the aluminum rod can be calculated using the equation a = F/m. Since the rod is moving at a constant velocity, the force due to air resistance can be ignored. Therefore, the force acting on the rod is solely due to the Lorentz force. Thus, we can write: a = F/m = qvBsinθ/m, Solving for q, we get: q = ma/vBsinθ = (0.946 x 10^-3 kg x 4.05 m/s)/(0.41 T x sin90o) = 9.26 x 10^-6 C.
Therefore, the charge of the particle on the aluminum rod is 9.26 x 10^-6 C.
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Consider a concave mirror that has a focal length f. In terms of f, determine the object distances that will produce a magnification of
A. -2
B. -3
C. -4
Answers
We have that the magnification of each focal length is given respectively as
A) has \(u=3\frac{f}{2}\)
B) has \(u=4\frac{f}{3}\)
C) has \(u=5\frac{f}{4}\)
From the question we are told that:
Focal Length F
Generally, the equation for Magnification is mathematically given by
\(M=\frac{-v}{u}\)
Therefore
\(v=2u\)
For A
\(M=-2\)
Therefore
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{2u}\)
Therefore
\(u=3\frac{f}{2}\)
For B
\(M=-3\)
Therefore
\(v=3u\)
Where
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{3u}\)
Therefore
\(u=4\frac{f}{3}\)
For C
\(M=-4\)
Therefore
\(v=4u\)
Therefore
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{4u}\)
Therefore
\(u=5\frac{f}{4}\)
Conclusion
From the calculations above we can rightly say that the magnifications of the values above are
A has \(u=3\frac{f}{2}\)
B has \(u=4\frac{f}{3}\)
C has \(u=5\frac{f}{4}\)
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Graph. See text version for more detail.
The graph above represents the nuclear decay of a radioactive element, measured using a radiation-detecting device. What is the half-life, in days, of this hypothetical element?
If the half-life of a given substance is 65 days, how long will it take for a 100-gram sample of the substance to decay until there is only 25 grams of the radioactive material remaining?
If a sample of radioactive isotopes takes 60 minutes to decay from 200 grams to 50 grams, what is the half-life of the isotope? Hint: First, determine how many times the sample has lost half of its mass, which tells you how many half-life cycles have occurred.
If a 500.0 g sample of technetium-99 decays to 62.5 g of technetium-99 remaining in 639,000 years, what is the half-life of technetium-99?
Answers
The half-life of hypothetical element technetium-99 is 210,936 years.
Half-life of the hypothetical element From the graph provided in the question, the half-life of the hypothetical element can be obtained by finding the time taken for the element to reduce to half its original quantity. Here, it can be seen from the graph that the quantity of the element reduces from 40 to 20 on day 4. Therefore, the half-life of the hypothetical element is 4 days.2. Time taken for a sample to decay from 100 grams to 25 gramsIf the half-life of a given substance is 65 days, then the quantity of the substance reduces to half every 65 days. From 100 grams to 50 grams, it takes one half-life cycle. From 50 grams to 25 grams, it will take another half-life cycle.
Therefore, it will take two half-life cycles, which is 2 × 65 = 130 days, for a 100-gram sample of the substance to decay until there is only 25 grams of the radioactive material remaining.3. Half-life of a sample that decays from 200 grams to 50 grams in 60 minutesIt is given that the sample of radioactive isotopes takes 60 minutes to decay from 200 grams to 50 grams. To find the half-life, we need to determine how many times the sample has lost half of its mass, which tells you how many half-life cycles have occurred.At 30 minutes, the sample reduces to half its original quantity, which is 100 grams. At 45 minutes, it reduces to 50 grams, which is half of 100 grams. Therefore, it takes two half-life cycles to reduce from 200 grams to 50 grams in 60 minutes. Hence, the half-life of the isotope is 15 minutes.4. Half-life of technetium-99 that decays from 500.0 g to 62.5 g in 639,000 yearsIt is given that a 500.0 g sample of technetium-99 decays to 62.5 g of technetium-99 remaining in 639,000 years. We can use the half-life formula to find the half-life of technetium-99.t1/2 = (t × log2) / log(N0 / Nt) Where,t1/2 = half-life of the substanceN0 = initial quantity of the substance Nt = quantity of the substance left after time t (in years)t = time (in years)From the given data,t1/2 = (639000 × log2) / log(500.0 / 62.5)t1/2 = 210,936 years.
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What is the resistance of a bulb of 4ow
connected in a line of 220v?
2
Answers
Answer:
1210 ohm
Explanation:
Given :
P=40 W
V=220 V
Now,
\(P=\frac{V^{2} }{R} \\40=\frac{(220)^{2} }{R} \\40R=48400\\R=\frac{48400}{40} \\R=1210 ohm\)
Therefore, resistance of bulb will be 1210 ohm
Heat can be transferred by conduction when one object is in direct contact with another object. Conduction can occur in solids, liquids, or gases, but it is more effective in A. gases because their particles are moving faster. B. liquids and gases because they occur at higher temperatures. C. liquids because they have a definite volume but not a definite shape. D. solids and liquids because their particles are arranged more closely together.
Answers
Answer:
The correct answer is D. solids and liquids because their particles are arranged more closely together.
How do the permanent magnets in an electric generator induce a current in a loop of wire that is moving between them?
A. The magnets cause charged particles within the wire to move as the poles of the magnets switch.
B. The moving electrons flow from the permanent magnets into the loop of wire.
C. The magnetic field of each magnet attracts the metal in the moving loop of wire.
D. The magnetic field between the magnets causes the charged particles within the wire to move.
Correct answer is D
Answers
The magnetic field between the magnets causes the charged particles within the wire to move.
According Faraday's law of electromagnetic induction, whenever their is a relative motion of a conductor is magnetic field, an emf will be induced in the conductor and the strength of the induced emf is directly proportional to the rate of change of magnetic flux linking the circuit.
The motion of the electrons is due to magnetic field created by the permanent magnet of the electric generator.
Thus, the magnetic field between the magnets causes the charged particles within the wire to move.
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One of the greatest dangers in a tornado is from flying objects. A 15 pound piece of lumber can turn into a flying missile that could severely damage walls and homes. A piece of steel with a mass of 200 pounds and travelling at the same velocity would cause even more damage. Select any evidence from the list below that you could use to explain why a 200 pound piece of steel would cause more damage than a 15 pound piece of wood travelling at the same velocity.
As the kinetic energy of an object increases, the force it can exert on another object decreases.
As the kinetic energy of an object increases, the force it can exert on another object increases.
Objects with more mass have less kinetic energy.
Objects with more mass have more kinetic energy.
As the velocity of an object increases, its kinetic energy decreases.
As the velocity of an object increases, its kinetic energy increases.
Answers
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Two uniform solid spheres, A and B have the same mass. The radius of sphere B is twice that of sphere A. The axis of rotation passes through the center of each sphere. Which one of the following statements concerning the moments of inertia of these spheres is true?
a. The moment of inertia of A is one-fourth that of B
b. The moment of inertia of A is one-half that of B
c. The moment of inertia of A is 5/4 that of B
d. The moment of inertia of A is 5/8 that of B
e. The two spheres have equal moments of inertia
Answers
Answer:
I = 2/5 M R^2 for solid sphere
IA = 2/5 M R^2
IB = 2/5 M (2 R)^2
IB / IA = 4
a. Sphere A has 1/4 the inertia of sphere B.
QUESTION 10
An archer fires an arrow towards a tree with initial speed 65 m/s and angle 25 degrees above the horizontal. If the arrow takes 0.85
seconds to hit the tree, calculate the horizontal distance between the archer and the tree.
QUESTION 11
A monkey throws a banana from a tree into a nearby river. The banana has initial speed 7.6 m/s, is angled 40 degrees below the
horizontal, and takes 0.75 seconds to land in the river. Calculate the speed of the banana when it hits the water.
Answers
Answer:
10) The distance between the archer and the tree is 50.074 meters.
11) The speed of the banana when it hits the water is approximately 13.554 meters per second.
Explanation:
10) The arrow experiments a parabolic motion, which is the combination of horizontal motion at constant velocity and vertical uniform accelerated motion. In this case we need to find the horizontal distance between the archer and the tree, calculated by the following kinematic equation:
\(x = x_{o} +v_{o}\cdot t \cdot \cos \theta\) (Eq. 1)
Where:
\(x_{o}\) - Initial position of the arrow, measured in meters.
\(x\) - Final position of the arrow, measured in meters.
\(v_{o}\) - Initial speed of the arrow, measured in meters per second.
\(t\) - Time, measured in seconds.
\(\theta\) - Launch angle, measured in sexagesimal degrees.
If we know that \(x_{o} = 0\,m\), \(v_{o} = 65\,\frac{m}{s}\), \(t = 0.85\,s\) and \(\theta = 25^{\circ}\), the horizontal distance between the archer and the tree is:
\(x = 0\,m + \left(65\,\frac{m}{s}\right)\cdot (0.85\,s)\cdot \cos 25^{\circ}\)
\(x = 50.074\,m\)
The distance between the archer and the tree is 50.074 meters.
11) The final speed of the banana (\(v\)), measured in meters per second, just before hitting the water is determined by the Pythagorean Theorem:
\(v = \sqrt{v_{x}^{2}+v_{y}^{2}}\) (Eq. 2)
Where:
\(v_{x}\) - Horizontal speed of the banana, measured in meters per second.
\(v_{y}\) - Vertical speed of the banana, measured in meters per second.
Each component of the speed are obtained by using these kinematic equations:
\(v_{x} = v_{o}\cdot \cos \theta\) (Eq. 3)
\(v_{y} = v_{o}\cdot \sin \theta +g\cdot t\) (Eq. 4)
Where \(g\) is the gravitational acceleration, measured in meters per square second.
If we know that \(v_{o} = 7.6\,\frac{m}{s}\), \(\theta = -40^{\circ}\), \(g = -9.807\,\frac{m}{s^{2}}\) and \(t = 0.75\,s\), the components of final speed are, respectively:
\(v_{x} = \left(7.6\,\frac{m}{s} \right)\cdot \cos (-40^{\circ})\)
\(v_{x} = 5.822\,\frac{m}{s}\)
\(v_{y} = \left(7.6\,\frac{m}{s}\right)\cdot \sin (-40^{\circ})+\left(-9.807\,\frac{m}{s^{2}} \right) \cdot (0.75\,s)\)
\(v_{y} = -12.240\,\frac{m}{s}\)
And the speed of the banana right before hitting the water is:
\(v = \sqrt{\left(5.822\,\frac{m}{s} \right)^{2}+\left(-12.240\,\frac{m}{s} \right)^{2}}\)
\(v \approx 13.554\,\frac{m}{s}\)
The speed of the banana when it hits the water is approximately 13.554 meters per second.
A wire loop in the shape of a circle spins in a uniform magnetic field. How does the torque on the loop change if the radius of the wire is doubled at the same time that the current flowing through the wire is quadrupled?
a. It increases by a factor of 2
b. It increases by a factor of 4
c. It increases by a factor of 8
d. t increases by a factor of 16
e. None of the above
Answers
The torque on the loop increases by a factor of 16.
option D.
What is the torque on wire loop?The torque on a wire loop in a magnetic field is given by the equation:
τ = NIABsinθ
Where;
τ is the torqueN is the number of turns in the wire loopI is the current flowing through the wireA is the area of the loopB is the magnetic field strengthθ is the angle between the magnetic field and the normal to the loopIf the radius of the wire is doubled, then the area of the loop becomes four times larger.
Also, if the current flowing through the wire is quadrupled, then the torque becomes four times larger.
The torque on the loop increases by a factor of 4 x 4 = 16.
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the weight of an object is measured in air to be 7N the object is then immersed in water and its apparent weight is measured to be 4N determined the buoyant force and state whether or not the object float
Answers
The buoyant force can be determined by subtracting the apparent weight of the object in water from its weight in air. In this case, the buoyant force would be 7N - 4N = 3N.
Based on the information provided, since the buoyant force (3N) is less than the weight of the object (7N), the object will not float.
Floating occurs when the buoyant force is greater than or equal to the weight of the object.
In this scenario, the object will experience a net downward force, indicating that it will sink rather than float in water.
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The energy lost during transformation is always in the form of:
chemical
heat
sunlight
mechanical
Answers
Answer:
heat
answer already there but yea just for da points
lithium nitride consists of two ions chemically bonded together what are the charges of each ion
Answers
Lithium nitride consists of two ions chemically bonded together. Lithium is an element that has a +1 charge, while nitrogen is an element that has a -3 charge. As a result, the lithium ion and the nitride ion have charges of +1 and -3, respectively. The chemical formula for lithium nitride is Li3N.
Lithium is a group 1 element, which means it has one valence electron. Nitrogen is a group 15 element, which means it has five valence electrons. Lithium and nitrogen chemically bond to form lithium nitride by sharing electrons from each element's valence shell. Since nitrogen has a higher electronegativity than lithium, it pulls the shared electrons closer to itself, resulting in a negative charge.
Nitride is a compound ion that is formed when a nitrogen atom gains three electrons. The electron configuration of nitrogen is 1s2 2s2 2p3, while the electron configuration of nitride is 1s2 2s2 2p6. Nitride, which has a -3 charge, is isoelectronic with neon and has a stable electron configuration. Lithium is a metal that belongs to the alkali metal family. Lithium has one electron in its outer shell, which it can donate to form a positive ion. As a result, lithium ions have a +1 charge.
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