a 120 nf capacitor is used in a standard 120 volt ac circuit with a frequency of 60 hz what is the cpaacitive resistance

Answers

Answer 1

To calculate the capacitive reactance (Xc) of a 120 nF capacitor in a standard 120 Volt AC circuit with a frequency of 60 Hz, you can use the following formula: Xc = 1 / (2π * f * C)

Where Xc is the capacitive reactance, f is the frequency (60 Hz), and C is the capacitance (120 nF, or 120 * 10^-9 F).
Following are the steps :
Step 1: Convert capacitance to farads: 120 nF = 120 * 10^-9 F = 1.2 * 10^-7 F
Step 2: Multiply the frequency (60 Hz) by 2π: 2π * 60 ≈ 377
Step 3: Multiply the result from step 2 by the capacitance: 377 * 1.2 * 10^-7 ≈ 4.5 * 10^-5
Step 4: Take the reciprocal of the result from step 3: 1 / (4.5 * 10^-5) ≈ 22226

Therefore, the capacitive reactance (Xc) in this circuit is approximately 22,226 ohms.

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Related Questions

abby volunteers at the planetarium at the museum of natural history. she is putting together a presentation about the solar system in which she will describe the shape of the solar system. she uses the term orbital plane when she discusses the plane in which the planets orbit.

Answers

Abby volunteers at the planetarium at the museum of natural history. she is putting together a presentation about the solar system in which she will describe the shape of the solar system. she uses the term orbital plane when she discusses the plane in which the planets orbit.

What is meant by the orbital plane?

The space that connects the centers of the orbiting objects and the object being orbited is known as an orbital plane and is formed like a flat, disk. Planets in our solar system avoid colliding with one another because their orbital planes are similar.

A rotating body's orbit is located in a geometric plane called the orbital plane. An orbital plane can be identified using just three non-collinear points in space. The locations of the centers of an orbiting celestial body and a large body (the host) at two different times or points in its orbit are typical examples.

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What are the three components of the cell theory

Answers

1. all living things are composed of cells
2. cells are the basic units of structure and function for living things
3. all cells come from pre-existing cells. (organisms grow by adding on more cells, not by increasing the sizes of the cell)

Answer:

The first component of the cell theory says that all living things are made of cells. The second component of the cell theory states that cells are the basic structure and function of living things. The last component of the cell theory says that cells come from other cells.

Explanation:

Srry this took so long but hope this helps this is also the right answer have a good day

(P.S please mark the helpfull )

what is the correct tight asymptotic bound for T(n) in 1,2,3 where T(1)=c ?
T(n) = 10T(n/10)+100n
T(n) =T(n/10)+100n
T(n) = T(n/10)+100

Answers

The correct tight asymptotic bound for T(n) in 1, 2, 3 where T(1)=c is Θ(n log n).

To find the tight asymptotic bound of T(n), we will use the Master Theorem. So, let's take a look at each recurrence relation:

1. T(n) = 10T(n/10)+100nApplying the Master Theorem: a = 10, b = 10, f(n) = 100nlogb a = log10 10 = 1 Since f(n) = Θ(n) = Θ(n1), Case 2 of the Master Theorem applies. The solution, therefore, is Θ(n log n).

2. T(n) = T(n/10)+100n Here, a = 1, b = 10, f(n) = 100nlogb a = log10 1 = 0 Since f(n) = Θ(n0) = Θ(1), Case 1 of the Master Theorem applies. The solution, therefore, is Θ(n).

3. T(n) = T(n/10)+100 Here, a = 1, b = 10, f(n) = 100logb a = log10 1 = 0 Since f(n) = Θ(1) = Θ(n0), Case 2 of the Master Theorem applies. The solution, therefore, is Θ(log n).Therefore, the correct tight asymptotic bound for T(n) in 1, 2, 3 where T(1)=c is Θ(n log n).

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Let's use the Master Theorem to find the asymptotic tight bound for each of the three recurrence relations given in the problem statement.

1. T(n) = 10T(n/10) + 100n Here, a = 10, b = 10, and f(n) = 100n. We can calculate the value of logb a as follows: log10 10 = 1 Since f(n) = Θ(n1), we can apply Case 2 of the Master Theorem and get: T(n) = Θ(n log n)Therefore, the correct tight asymptotic bound for T(n) in the first case is Θ(n log n).

2. T(n) = T(n/10) + 100n Here, a = 1, b = 10, and f(n) = 100n. We can calculate the value of logb a as follows: log10 1 = 0 Since f(n) = Θ(n1), we can apply Case 1 of the Master Theorem and get: T(n) = Θ(n)Therefore, the correct tight asymptotic bound for T(n) in the second case is Θ(n).

3. T(n) = T(n/10) + 100 Here, a = 1, b = 10, and f(n) = 100. We can calculate the value of logb a as follows: log10 1 = 0 Since f(n) = Θ(1), we can apply Case 2 of the Master Theorem and get: T(n) = Θ(log n) Therefore, the correct tight asymptotic bound for T(n) in the third case is Θ(log n). Hence, the three asymptotic tight bounds for T(n) are Θ(n log n), Θ(n), and Θ(log n), respectively.

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A student fills a plastic bottle full of water. There are two holes one at the bottom and second at the half way up. Why water comes out at right angles to the bottle.
PLZ ANSWER

Answers

Answer:

Due to the direction of force due to pressure.

Explanation:

Let there be two small holes having area, \(a\) , at points A and B in the bottle filled with water as shown in the figure \((i)\). Water comes out at the right angles to the wall of the bottle as shown in figure \((ii)\).

From Newton's second law, the acceleration of an object is always in the direction of net applied force.

We know that pressure, \(P\), on any surface due to fluid acts perpendicular to the surface, so, the force due to pressure,\(F=Pa\), will also be perpendicular to the surface as shown in the diagram\((iii)\).

So, the direction of the acceleration of the water element at that point will be perpendicular to the bottle surface which leads to the change in velocity of the water element in the same direction.

That's why water comes out at right angles to the surface of the bottle.

A student fills a plastic bottle full of water. There are two holes one at the bottom and second at the

Question 2 (1 point)
This graph shows an object in free fall. Assume there is no air resistance. What is the only force acting on this object?

Question 2 (1 point)This graph shows an object in free fall. Assume there is no air resistance. What

Answers

Answer:

Actually, there is  no force (felt by the object) acting on the object.

It is similar to an  object in orbit around the earth (weightlessness)

F = M a    describes the motion of the particle where

M a = M g    where the acceleration of the particle is equal to the force of gravity acting on the particle

From an external view the only force acting on the particle is M g and it produces an acceleration of M g

There is no force felt by the freely falling body. The cause of free fall is gravitational pull. Where Acceleration is equal to the gravitational acceleration. According to Newton's Law of Gravitation , two bodies attract each other due to their masses and separation , since earth is a very big body therefore the lit body falls towards the earth . Thus the graph plotted is a straight line.

What is Newton's law of Gravitation?

"The force acting between two bodies is directly proportional to product of masses and inversely proportional to the square of the separation ."

F= G.{m_{1} . m_{2} }/r^{2}.

Hence the only force by which the object is falling is gravitational pull.

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A2
Need 100% perfect answer in 20 minutes.
Please please solve quickly and perfectly.
Write neat.
I promise I will rate positive.a) Write down the truth tables for the NAND gate and the NOR gate with two inputs. [4 marks] b) Write down a truth table for the function Z in terms of the inputs A, B and C. Also write a logic expression for Z in terms of A, B and C. D U B Z С S (11 marks] c) Use de-Morgan's laws to simplify the following Boolean expression Q = (A. (A + C))' 15 marks

Answers

The simplified expression for Q using De Morgan's laws is Q = A . (A' . C')'.

a) Truth tables for the NAND gate and NOR gate with two inputs:

NAND gate:

| A | B | Q |

|---|---|---|

| 0 | 0 | 1 |

| 0 | 1 | 1 |

| 1 | 0 | 1 |

| 1 | 1 | 0 |

NOR gate:

| A | B | Q |

|---|---|---|

| 0 | 0 | 1 |

| 0 | 1 | 0 |

| 1 | 0 | 0 |

| 1 | 1 | 0 |

b) Truth table and logic expression for Z in terms of inputs A, B, and C:

| A | B | C | Z |

|---|---|---|---|

| 0 | 0 | 0 | 1 |

| 0 | 0 | 1 | 0 |

| 0 | 1 | 0 | 1 |

| 0 | 1 | 1 | 0 |

| 1 | 0 | 0 | 1 |

| 1 | 0 | 1 | 0 |

| 1 | 1 | 0 | 0 |

| 1 | 1 | 1 | 0 |

Logic expression for Z: Z = (A' AND B' AND C) OR (A' AND B AND C')

c) Simplification of the Boolean expression Q = (A. (A + C))' using De Morgan's laws:

Q = (A. (A + C))'

Apply De Morgan's law: (AB)' = A' + B'

Q = (A' + (A + C)')'

Apply De Morgan's law again: (A + B)' = A' . B'

Q = ((A')' . (A + C)')'

Simplifying the double negations: (A')' = A and (A + C)' = A' . C'

Q = (A . (A' . C'))'

Final simplified expression: Q = A . (A' . C')'

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If star A is 20 light years away from earth and star B is 40 light years away from earth,which star appears brighter and by what factor?

Answers

Answer:

Because Star A and Star B have identical luminosities, the difference in their apparent brightness is due solely to distance. Star B is twice as far from Earth as Star A.

Explanation:

A 6.8 kg cannon ball leaves a canon with a speed of 188 m/s. Find the average net force applied to the ball if the cannon muzzle is 4.2 m long.


i want the answer with the steps ​

Answers

Answer:

 its not long dummy, its your imagination

Explanation:

The electric force between two charges increases when
A) both charges become negative
B) both charges become positive
C) the charges get closer together
D) the charges get further apart

Answers

Answer:

the charges get closer together

d!!!!!!!!!!.!!!!!!!........d

The image shown is an illustration of Kepler’s second law. An illustration with a circle representing the sun and a smaller circle representing a planet. The sun is at a focus of a draw ellipse that the planet is on. There are lines drawn radially out from the Sun to the elliptical path of the planet. The planet is at the part of the ellipse that is closest to the sun. The position of the planet is labeled W and the position opposite the planet is labeled Z. The line closest to W is labeled X and the line closest to Z is labeld Y. Which conclusion is best supported by the image? The gravitational force at W is less than the gravitational force at Y. The time needed to travel from W to X is the same as the time needed to travel from Y to Z. The gravitational force at W is the same as the gravitational force at Y. The time needed to travel from W to X is greater than the time needed to travel from Y to Z.

Answers

Answer:

B; the time needed to travel from W to X is the same as the time needed to travel from Y to Z.

Explanation:

According to Kepler's Second Law, the time it takes to travel each sweep of area is equal, the same way the area of each section is also equal. Also, this answer is correct on Edge.

Answer:

The answer is B !

Explanation:

I took the test and got it correct

An atom of xenon has a mass number of 127 amu. How many neutrons
does it contain? *

An atom of xenon has a mass number of 127 amu. How many neutronsdoes it contain? *

Answers

Answer:

73 neutrons.

Explanation:

Data obtained from the question:

Mass number of Xenon = 127.

Neutron number =...?

We can obtain the number of neutron present as follow:

Atomic number of Xenon = 54

Recall:

Atomic number = proton number = 54

Mass number = proton + neutron

127 = 54 + Neutron

Neutron = 127 – 54

Neutron = 73.

Therefore, 73 neutrons are present in the Xenon atom.

An escalator is used to move 25 passengers every minute from the first floor of a department store to the second. The second floor is located 5.30 meters above the first floor. The average passenger's mass is 60 kg. Determine the power requirement of the escalator in order to move this number of passengers in this amount of time.
Please help me quickly!

Answers

Answer:

1298.5watt

Explanation:

Power is defined as the rate at which work is done

Expressed mathematically as;

P = F × d/ t; F = force or weight of object ;d is height or distance sustain and t is time covered

Hence for 1 person the power consumption is ;

Note weight =mass× acceleration of free fall due to gravity,g

g is known as 9.8m/S2

Time taken is 1min which is 60 sec

60 ×9.8 × 5.3/60 = 51.94 watt

Hence for 25 persons we have

25 × 51.94 =1298.5watt

1.3kilo watt( kilo is 1000)

The work done by the escalator is 3,080.4 joules and the power requirement of the escalator to move 25 passengers every minute is approximately 51.34 watts.

The Work Done is calculated as:

Force (F) = 60 × 9.8

Distance (d) = 5.30 meters

Work (W) = F × d

Work (W) = (60 × 9.8) × 5.30

Work (W) = 3,080.4 joules

The Power is calculated as:

Time (t) = 1 minute

Power (P) = Work / Tim (t)

Power (P) = 3,080.4 / 60

Power (P) = 51.34 watts

Therefore, the power requirement of the escalator to move 25 passengers every minute is approximately 51.34 watts.

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what is the standard measurement system used by scientists around the world?

Answers

Answer:

Hey mate....

Explanation:

This is ur answer....

The International System of Units (SI), commonly known as the metric system, is the international standard for measurement.

Hope it helps!

Brainliest pls!

Follow me! ◇

International system of units.French système international d'Unitès, international decimal system of weights and measures derived from and extending the metric system of units.Adopted by the 11th General conference on weights and measures (CGPM) in 1960, It is abbreviated SI in all languages.

You have a light spring which obeys Hooke's law. This spring stretches 2.28 cm vertically when a 2.40 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) N/m (b) the distance (in cm) the spring stretches if you replace the 2.40 kg object with a 1.20 kg object cm (c) the amount of work (in J) an external agent must do to stretch the spring 8.70 cm from its unstretched position J

Answers

(a) To determine the force constant (k) of the spring, we will use Hooke's Law, which states that the force exerted by a spring (F) is proportional to the displacement (x) from its equilibrium position:

F = -kx

First, we need to calculate the gravitational force (weight) acting on the 2.40 kg object:

F = mg
F = (2.40 kg)(9.81 m/s²)
F ≈ 23.544 N

Now, we can use Hooke's Law to find the force constant (k):

23.544 N = k(0.0228 m)
k ≈ 1032 N/m

(b) To find the distance the spring stretches with a 1.20 kg object, we'll use the same formula:

F = (1.20 kg)(9.81 m/s²)
F ≈ 11.772 N

Now, rearrange Hooke's Law to solve for x:

x = F/k
x ≈ 11.772 N / 1032 N/m
x ≈ 0.0114 m or 1.14 cm

(c) To calculate the work (W) done by an external agent to stretch the spring 8.70 cm, we'll use the formula for the work done on a spring:

W = (1/2)kx²

First, convert the distance to meters:

x = 8.70 cm = 0.087 m

Now, calculate the work:

W = (1/2)(1032 N/m)(0.087 m)²
W ≈ 3.918 J

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A centripetal force of 250 N is exerted on a 2.2 kg discus as it rotates uniformly in a horizontal circle of radius 0.85 m. Calculate the speed of the discus in both m/s and rotations per minute?

Answers

Answer:

133m/s

Explanation:

b/c 250÷2.2÷0.85=133

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hey plz solve this question I will mark as the brillianest plzzzzzzzzzzzzzzzzzzzz

Answers

Explanation:

I hope it helped U

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A baseball player pitches a 0. 14 kg baseball 30. 0 m/s. Calculate the kinetic energy for the baseball.

Answers

The kinetic energy of the baseball with a mass of 0.14 Kg and 30 m/s speed is 63 J.

What is kinetic energy?

Kinetic energy of an object is generated by virtue of its motion. It is dependant on the mass and speed of the object. Thus as mass or speed increases, kinetic energy increases.

The equation connecting the kinetic energy with the mass and speed , v is given as follows:

Ke = 1/2 m v²

Given that the mass = 0.14 kg

speed = 30 m/s.

kinetic energy = 1/2 0.14 × 30² = 63 J.

Therefore, the kinetic energy of the baseball is 63 J.

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A police officer on a mountain bike is cruising at a speed of 3.50m/s, when he sees a wanted
criminal, standing on a corner, 75m ahead of him. If the police officer accelerates at a rate of
2.00m/s^2, how much time will he take to reach the corner?

Answers

Answer:

7 seconds

Explanation:

please see paper!

A police officer on a mountain bike is cruising at a speed of 3.50m/s, when he sees a wantedcriminal,

vf² = vo²+2ad

vf=vo+at

vf²=3.5²+2.2.75

vf²=312.25

vf=17.67 m/s

vf=vo+at

17.67 = 3.5 +2t

t=7.085 s

To win the game, a place kicker must kick a
football from a point 25 m (27.34 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 17 m/s at
an angle of 42.2◦ from the horizontal.
The acceleration of gravity is 9.8 m/s2.

By how much vertical distance does the ball
clear the crossbar?
Answer in units of

Answers

okay so i do not know how to do this

In the qualifying round of the 50-meter freestyle in the sectional swimming championship, Dugan got an early lead by finishing the first 25 m in 10.08 seconds. Dugan finished the return leg (25 m distance) in 10.17 seconds.

a. Determine Dugan's average speed for the entire race.

b. Determine Dugan's average speed for the first 25.00 m leg of the race.

c. Determine Dugan's average velocity for the entire race

Answers

Answer:

a. Dugan's average speed for the entire race was 2.47 m/s.

b. Dugan's average speed for the first 25.00 m leg of the race was 2.48 m/s.

c. Since the starting and ending points are the same, the displacement is zero. Therefore, the average velocity is also zero.

Explanation:

To solve this problem, we'll need to use the formula:

average speed = total distance / total time

where total distance is the distance covered in the entire race (50 meters), and total time is the time it took Dugan to cover that distance.

a. To find Dugan's average speed for the entire race, we'll need to add up the times for both legs of the race:

total time = 10.08 seconds + 10.17 seconds = 20.25 seconds

Now we can plug in the values:

average speed = 50 meters / 20.25 seconds = 2.47 m/s

So Dugan's average speed for the entire race was 2.47 m/s.

b. To find Dugan's average speed for the first 25.00 m leg of the race, we'll need to use the formula again, but this time we'll only consider the first leg of the race:

average speed = 25 meters / 10.08 seconds = 2.48 m/s

So Dugan's average speed for the first 25.00 m leg of the race was 2.48 m/s.

c. Average velocity is the displacement (change in position) divided by the time taken. Since the starting and ending points are the same, the displacement is zero. Therefore, the average velocity is also zero.

Answer:

the guy above is actually right :)

Explanation:

What is the net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons to the left?.

Answers

The net force on an object is zero that is pulled with forces of 80 newtons to the right and 80 newtons to the left.

Net force is equal to sum of all the force acting on a body.

The formula for net force if n force are acting on it:

                       \(F_{net}=F_{1}+ F_{2}+F_{3}.....F_{n}\)

In this case the two forces are equal but opposite in direction.

Putting the values in the formula

\(F_{net} = 80+(-80)\) (since forces are equal but opposite)

\(F_{net}= 0\)

So the net force acting on the object is zero because the forces are equal and opposite.

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The net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons to the left is: 0 newtons

To solve this problem the formula of net force and the procedure that we have to use is:

Fr = ∑F

Where:

Fr = resultant force∑Fr = F1 + F2 + Fn

Information about the problem:

F1 = 80 newtonsF2 = - 80 newtonsFr = ?

Applying the resultant force formula we get:

Fr = ∑F

Fr = F1 + F2

Fr = 80 newtons - 80 newtons

Fr= 0 newtons

What is resultant force?

We can say that the resultant force is the algebraic sum of all the forces acting on a body.

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What is the net force on an object that is pulled with forces of 80 newtons to the right and 80 newtons

A point charge with charge q1 = 2.40 μC
is held stationary at the origin. A second point charge with charge q2
= -4.90 μC moves from the point (0.170 m, 0) to the point (0.230 m , 0.270 m ).

How much work is done by the electrostatic force on the moving point charge?
Express your answer in joules.

Answers

The work done by the electrostatic force on the moving point charge is 1.014 J.

Displacement of the second charge

d = √[(0.23 - 0.17)² + (0.27 - 0)²] = 0.277 m

Force between the two charges

F = kq₁q₂/r²

where;

q₁ is magnitude of first chargeq₂ is magnitude of second charger is the distance between the two chargesk is Coulomb's constant

F = (9 x 10⁹ x 2.4 x 10⁻⁶ x 4.9 x 10⁻⁶)/(0.17)²

F = 3.66 N

Work done in moving the point charge

W = Fd

W = 3.66 x 0.277

W = 1.014 J

Thus, the work done by the electrostatic force on the moving point charge is 1.014 J.

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PLS HELP DUE IN 20 MINS!!! True or false: You can make a pulse travel at a faster speed without changing the shape or size of the pulse.

Answers

Answer:

False

Explanation:

A Larger pulse with more energy means that the wave has a large amplitude. As in the given question, both the waves are travelling in the same medium, hence their speeds will remain the same and therefore the larger pulse will not overtake the smaller pulse. Remember the amplitude of a wave does not affect the speed at which the wave travels.

a baseball is dropped from a hight of 5m as the ball falls toward earth there is an increase in its ___ ?? please help​

Answers

I think is Air resistance

Two forces of
411
N and
617
N act on an object. The angle between the forces is
46°.
Find the magnitude of the resultant and the angle that it makes
with the larger force.

Answers

Let's first resolve the two forces into their components as shown in the diagram below: The larger force (617 N) makes an angle of 46° with the horizontal axis.

Therefore, the horizontal component will be given by:

H = 617 cos 46°H = 617 × 0.69H = 425.73 N

The vertical component will be given by:V = 617 sin 46°V = 617 × 0.73V = 450.66 NOn the other hand, the smaller force (411 N) makes an angle of (90° - 46°) = 44° with the horizontal axis. Therefore, the horizontal component will be given by:H = 411 cos 44°H = 411 × 0.72H

= 296.52 N

The vertical component will be given by:V = 411 sin 44°V = 411 × 0.67V = 274.47 N The resultant horizontal component, R will be given by:R = 425.73 + 296.52R = 722.25 N The resultant vertical component, R will be given by:R = 450.66 + 274.47R = 725.13 N The magnitude of the resultant, R will be given by:R² = (722.25)² + (725.13)²R = √(522198.06)R = 722.82 N The angle that R makes with the larger force (617 N) will be given by:θ = tan⁻¹(725.13/722.25)θ = 45.23° Therefore, the magnitude of the resultant is 722.82 N and it makes an angle of 45.23° with the larger force.

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the actuon of a lever is affected by the?

Answers

The answer is pulley

a baseball weighs 5.13 oz. what is the kinetic energy in j of this baseball when it is thrown by a major-league pitcher at 95.0 mph

Answers

The kinetic energy of the baseball when thrown by a major-league pitcher at 95.0 mph is approximately 136.22 Joules.

The kinetic energy (KE) of an object can be calculated using the formula KE = 0.5 * m * v^2, where m is the mass in kilograms, and v is the velocity in meters per second.

First, we need to convert the mass from ounces to kilograms and the velocity from miles per hour to meters per second.

1 oz = 0.0283495 kg

5.13 oz * 0.0283495 = 0.14515 kg

1 mph = 0.44704 m/s

95.0 mph * 0.44704 = 42.4698 m/s

Now, we can calculate the kinetic energy:

KE = 0.5 * 0.14515 kg * (42.4698 m/s)^2

KE ≈ 136.22 Joules

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If a ball is thrown straight up into the air with an initial velocity of $60{ft} /{s}$, its height in feet after $t$ second is given by $y=60 t-16 t^2$. Find the average velocity (include units, help (units)) for the time period begining when $t=2$ seconds and lasting
(i) 0.5 seconds
Avenge velocity:
(ii) 0.1 seconds
Average velocity:
(iii) 0.01 seconds
Average velocity:
Finally based on the above results, guess what the instantaneous velocity of the ball is when $t=2$. Average velociry:

Answers

The instantaneous velocity of the ball is when $t=2$ is 32 ft/s so the average velocity: 32 ft/s.

The given function is $y=60t-16t^2$. We need to find the average velocity of the ball for the time period beginning when $t=2$ seconds and lasting. The average velocity is calculated by dividing the distance travelled by the time taken. The average velocity for the time period beginning when $t=2$ seconds and lasting 0.5 seconds is calculated as follows:

Average velocity = $[\frac{y_2-y_1}{t_2-t_1}]$Here, $y_2$ is the value of the function when $t=2.5$ and $y_1$ is the value of the function when $t=2$. Therefore, $y_2=60(2.5)-16(2.5)^2=45$ and $y_1=60(2)-16(2)^2=32$.The time taken is $0.5$ seconds. Average velocity = $[\frac{y_2-y_1}{t_2-t_1}]$Average velocity = $[\frac{45-32}{0.5}]$Average velocity = $[\frac{13}{0.5}]$Average velocity = $26$ ft/sNow, for the time period beginning when $t=2$ seconds and lasting(ii) 0.1 seconds. Here, $y_2$ is the value of the function when $t=2.1$ and $y_1$ is the value of the function when $t=2$. Therefore, $y_2=60(2.1)-16(2.1)^2=31.84$ and $y_1=60(2)-16(2)^2=32$.The time taken is $0.1$ seconds. Average velocity = $[\frac{y_2-y_1}{t_2-t_1}]$Average velocity = $[\frac{31.84-32}{0.1}]$Average velocity = $[-1.6]$ ft/s(iii) 0.01 seconds. Here, $y_2$ is the value of the function when $t=2.01$ and $y_1$ is the value of the function when $t=2$. Therefore, $y_2=60(2.01)-16(2.01)^2=31.9364$ and $y_1=60(2)-16(2)^2=32$.The time taken is $0.01$ seconds. Average velocity = $[\frac{y_2-y_1}{t_2-t_1}]$Average velocity = $[\frac{31.9364-32}{0.01}]$Average velocity = $[-6.36]$ ft/s

Finally based on the above results, we can guess that the instantaneous velocity of the ball is when $t=2$ is 32 ft/s. hence, Average velocity: 32 ft/s.

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