Lab report on motion 6th grade

Answer:

The characteristics that determine how easily two substances change temperature are:

The volume and density of the substances and the amount of time they are in contact do not directly affect how easily they change temperature.

Explanation:

The value of  the missing resistance, R₃ = 10.35 ohms.

The value of the missing voltages, V₁ = 6 V, V ₃ = 24 V.

The value of the missing currents, I₁ = 3 A, I₃ = 2.32 A.

The values of the missing component of the circuit is calculated by applying the following formula.

The total resistance of the circuit;

For R₂, R₃, 1/R = 1/R₂ + 1/R₃

1/R = 1/12 +  1/R₃

1/R = (R₃ + 1)/(12R₃)

R = 12R₃ / (R₃ + 1)

For, R₁, R₂ and R₃, total resistance;

R = 12R₃ / (R₃ + 1) + R₁

R = [12R₃ / (R₃ + 1)] + 2

R = (12R₃ + 2(R₃ + 1) ) / (R₃ + 1)

R = (12R₃ + 2R₃ + 2 ) / (R₃ + 1)

R = (14R₃ + 2 ) / (R₃ + 1)

The total current in circuit is calculated as;

I = V/R

I = 30 / R

I = ( 30 ) / (14R₃ + 2 ) / (R₃ + 1)

I = (30R₃ + 30) / (14R₃ + 2) ------- (1)

The voltage in parallel circuit is the same

V₂ = V₃ = 24 V

V₃ = IR₃

24 = IR₃

I = 24/R₃  --------- (2)

Solve (1) and (2) together as follows;

24/R₃ = (30R₃ + 30) / (14R₃ + 2)

30R₃² - 306R - 48 = 0

Solve the quadratic equation, using formula method.

R₃ = 10.35 ohms

I₃ = V₃/R₃

I₃ = 24 V / 10.35

I₃ = 2.32 A

If the voltage drop at R₂ and R₃ = 24 V, the voltage drop at R₁ = 30V - 24 V = 6 V

The current in R₁ = V₁/R₁ = 6 V / 2 V = 3 A

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Answer:

\(a=-0.001388\ m/s^2\)

Explanation:

Given that,

Initial speed of a train, u = 2.5 m/s

Finally, it reaches the station, v = 0 (at rest)

Time, t = 30 minutes = 1800 s

Acceleration is equal to the rate of change of velocity. So,

\(a=\dfrac{v-u}{t}\\\\a=\dfrac{0-2.5}{1800}\\\\a=-0.001388\ m/s^2\)

So, its acceleration is \(0.001388\ m/s^2\).

Answer:

A

Explanation:

edge 2020

The horizontal acceleration of a ball that is launched horizontally with a velocity of 5.6 m/s will be zero. Option B is correct.

The motion of an item hurled or projected into the air, subject only to gravity's acceleration, is known as projectile motion.

The item is known as a projectile, and the course it takes is known as a trajectory. Falling object motion is a simple one-dimensional kind of projectile motion with no horizontal movement.

The projectile's motion is divided into two parts: horizontal and vertical motion.

The horizontal acceleration of a ball that is launched horizontally with a velocity of 5.6 m/s will be zero.

Hence, option B is correct.

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From the question;

1) It takes 15.75 years to decrease to 1/8

2) It takes 8.36 years to decrease to 1/3

Half-life is the length of time it takes for a chemical to degrade or go through a particular process. It frequently refers to the length of time it takes for half of a radioactive substance to decay into a stable form in the context of radioactive decay.

We know that;

\(N/No = (1/2)^t/t1/2\)

No = initial amount

N = amount at time t

t = Time taken

t1/2 = half life

\(1/8 = (1/2)^t/5.252^-3 = 2^-t/5.25\)

t = 15.75 years

Again;

\(1/3 = (1/2)^t/5.25\)

ln0.33 = t/5.25ln0.5

t = ln0.33/ln0.5 * 5.25

t = 8.36 years

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When people become dependent on their partners and don't want to leave them, it can have a variety of negative consequences for their physical, emotional, and mental health.

Firstly, dependency can cause a loss of personal identity and self-esteem. When individuals become overly dependent on their partners, they may begin to define themselves solely in terms of their relationship. This can lead to a loss of personal identity and a decrease in self-esteem, as they feel that they cannot function independently.

Secondly, dependency can create a power imbalance in the relationship. The partner who is more dependent may feel that they have to do whatever it takes to keep their partner happy and maintain the relationship. This can lead to a sense of powerlessness and a lack of control over their own lives, which can be damaging to their mental health.

Thirdly, dependency can cause individuals to tolerate unhealthy or abusive behaviors from their partner. When individuals become too dependent on their partners, they may fear losing them and therefore tolerate behaviors that are unhealthy or even abusive. This can have serious negative consequences for their physical and mental health, as well as their overall well-being.

Finally, dependency can make it difficult to leave an unhealthy relationship. Individuals who are overly dependent on their partners may fear being alone, and may feel that they cannot function without their partner. This can make it difficult to leave an unhealthy or abusive relationship, even when it is necessary for their well-being.

Overall, becoming overly dependent on a partner can have serious negative consequences for an individual's physical, emotional, and mental health. It is important for individuals to maintain a sense of personal identity and independence, and to recognize when a relationship is unhealthy or abusive, so that they can take steps to protect their well-being.

Answer:

The aceleration of an object is in the direction of the net force. If you push or pull an object in a particular direction, it accelerates in that direction. The aceleration has a magnitude directly proportional to the magnitude of the net force.

Explanation:

Hope this helps Plz mark brainliest

Answer:

Kinetic and potential

potential (didnt say its moving)

Kinetic and potential

kinetic

kinetic

kinetic

potential

kinetic and potential

kinetic (might have potential)

kinetic

sorry, it's B, not a made a mistake in the approximation

Answer:

1. Mechanical wave

2. Longitudinal wave

3. The cochlea

4. The diagram is not attached so far

5. the wavelength decreases.

6. slowest through gases, faster through liquids, and fastest through solids. or simply solids>liquids>gases

Explanation:

Greetings!!

1. Waves in water and sound waves in air are two examples of mechanical waves. Mechanical waves are caused by a disturbance or vibration in matter, whether solid, gas, liquid, or plasma.

2. Sound is a longitudinal wave.

3. The cochlea is filled with a fluid that moves in response to the vibrations from the oval window. As the fluid moves, 25,000 nerve endings are set into motion. These nerve endings transform the vibrations into electrical impulses that then travel along the eighth cranial nerve (auditory nerve) to the brain.

4.

5. As the frequency increases, the wavelength decreases.

6. The Speed of Sound: Sound travels at different speeds depending on what it is traveling through. Of the three mediums (gas, liquid, and solid) sound waves travel the slowest through gases, faster through liquids, and fastest through solids.

Hope it helps!!!!

Answer:

Explanation:

From the question we are told that

Constant speed =48mile/hr

Diameter of a wheel = 22inch therefore \(r=\frac{22}{2} =>11\)

Generally Convert from mile/hr to inches/sec

The length in inches is equal to the miles multiplied by 63,360.

an hour is 3600seconds

\(\frac{48*63360}{3600}\)

48miles/h = 849.8 inch/sec

\(V_a =844.8 inch/sec\)

therefore

\(\omega= \frac{v}{r}\)

\(\omega= \frac{844,8}{11}\) =>\(76.8 sec ^-^1\)

a)Considering the velocity of Vb  in inches per seconds

Generally the formula is stated as

\(V_b= V_a + V_b_/_a\)

\(V_b = 844.8 + \omega r\)

\(V_b= 1639.6in/s\)

b)Considering the velocity of Vc  in inches per seconds

Since the tire doesn't slip as earlier stated in the question

Therefore \(V_c = 844.8 -w(r) =0\)

c)Considering the velocity of Ve  in inches per seconds

Generally the formula is stated as

\(V_e=V_a + V_e_/_a\)

\(V_e = 844.8 \uparrow \theta -844.8 \uparrow = 844.8\sqrt{2}\)

Expressing result with vector

\(V_e =844.54 + 20.85j\)

d)Considering the velocity of Vd  in inches per seconds

Generally the formula is stated as

\(V_d= V_a + V_d_/_a\)

Mathematically

\(V_d =844.8 \uparrow +( 844.8\frac{\sqrt{3} }{2} \uparrow + \frac{844.8}{2} \uparrow)\)

\(V_d= (1576.4 \uparrow + 422.4\uparrow)\)

\(V_d= 1632.028in/s\)

Based on the information, it should be noted that the resistance R is 0.5 Ω.

When S1 and S2 are open, i leads e by 30°. In this case, the circuit consists of only the inductor (L) and the capacitor (C) in series. Therefore, the impedance of the circuit can be written as:

Z = jωL - 1/(jωC)

Since i leads e by 30°, we can express the phasor relationship as:

I = k * e^(j(ωt + θ))

Z = jωL - 1/(jωC) = j(120π)L - 1/(j(120π)C)

Re(Z) = 0

By equating the real parts, we get:

0 = 0 - 1/(120πC)

Let's assume that there is a resistance (R) in series with the inductor and capacitor. The impedance equation becomes:

Z = R + jωL - 1/(jωC)

Z = R + jωL

Im(Z) = ωL > 0

Substituting the angular frequency and rearranging the inequality, we have:

120πL > 0

L > 0

This condition implies that the inductance L must be greater than zero.

When S1 and S2 are closed, i has an amplitude of 0.5 A. In this case, the impedance is:

Z = R + jωL - 1/(jωC)

Since the amplitude of i is given as 0.5 A, we can express the phasor relationship as:

I = 0.5 * e^(j(ωt + θ))

By substituting this phasor relationship into the impedance equation, we can determine the value of R. The real part of the impedance must be equal to R:

Re(Z) = R

Since the amplitude of i is 0.5 A, the real part of the impedance must be equal to 0.5 A: 0.5 = R

Therefore, the resistance R is 0.5 Ω.

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Answer:

Approximately \(3.7\; {\rm kg}\).

Explanation:

The free-fall acceleration is equal to the gravitational field strength at that position. It is given that the free-fall acceleration on planet B is \(0.802\, (9.8\; {\rm m\cdot s^{-2}}) \approx 7.87\; {\rm m\cdot s^{-2}}\). The gravitational field strength on that planet would have the same value: approximately \(7.87\; {\rm m\cdot s^{-2}}\).

Note that \(1\; {\rm N} = 1\; {\rm kg\cdot m\cdot s^{-2}}\). Thus:

\(\begin{aligned} 7.87\; {\rm m\cdot s^{-2}} &= 7.87\; {\rm m\cdot s^{-2}\cdot (kg\cdot kg^{-1})} \\ &= 7.87\; {\rm (kg \cdot m\cdot s^{-2})\cdot kg^{-1}} \\ &= 7.87\; {\rm N\cdot kg^{-1}} \end{aligned}\).

In other words, on this planet, the weight on every \(1\; {\rm kg}\) of mass would be \(7.87\; {\rm N}\).

Divide the gravitational attraction (weight) on the object by the gravitational field strength to find the mass of this object:

\(\begin{aligned}(\text{mass}) &= \frac{(\text{weight})}{(\text{gravitational field strength})} \\ &\approx \frac{29.1\; {\rm N}}{7.87\; {\rm N\cdot kg^{-1}}} \\ &\approx 3.7\; {\rm kg}\end{aligned}\).

Taking half of the given length and pulling it to a length of 2L as before, the frequency obtained by vibrating in the basic method is 6fo. option(ii)

When a bow vibrates in its fundamental mode with a length of 2L, the frequency is denoted as f. Now, let's consider the scenario where half of the given length (L) is pulled to a length of 2L.

In the fundamental mode of vibration, the frequency is inversely proportional to the length of the vibrating object. Therefore, if the length of the bow is halved to L, the frequency would double to 2f.

When this new length of L is pulled to a length of 2L, we need to determine the frequency obtained in the fundamental mode.

Since the frequency is inversely proportional to the length, we can use the inverse relationship to find the new frequency.

If the original frequency was 2f at length 2L, when the length is reduced to L, the new frequency would be (2f)/(2L) = f/L.

Now, if this length of L is stretched to 2L again, the new frequency in the fundamental mode would be (f/L) * (2L) = 2f. option(ii)

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The purpose of the antireflective coating on the glass layer of a solar

the cell is that It allows more solar energy to be absorbed, therefore the correct answer is option D.

The energy emitted by the Sun as a form of thermal electromagnetic radiation is known as solar energy.

This solar energy is produced by nuclear fusion in the center of the Sun. Solar energy is a form of renewable source of energy.

As given in the problem statement we have to find out the best statement from the given options which describes the purpose of the antireflective coating on the glass layer of a solar cell.

In order to increase the amount of solar energy that can be absorbed, a solar cell's glass layer has an anti-reflective coating, therefore the correct answer is option D.

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Answer:

D

Explanation:

Explanation:

the speed of the light is

the time in a year is

the distance traveled by the light is

Plugging all the values in the above relation, we get

now convert this into miles.

now the distance is,

Thus, the distance traveled by the light in a year is 6 billion.

The resultant of two displacement vectors having opposite directions is the difference of the two displacements, having the same direction as the smaller vector.

When two displacement vectors have opposite directions, it means they are pointing in opposite ways. In other words, one vector is in the opposite direction of the other. To find the resultant of these vectors, we need to subtract one vector from the other.

If we consider two displacement vectors, let's say vector A and vector B, and they have opposite directions, we can represent them as A and -B.

To find the resultant, we subtract vector B from vector A: A - (-B) or A + B.

The resultant will have the same direction as the smaller vector. This is because when we subtract a larger vector from a smaller vector, the resultant will have the direction of the smaller vector.

Therefore, the correct option is: "The resultant is the difference of the two displacements, having the same direction as the smaller vector."

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Answer: The answer is C i believe

Since the toboggan is sliding through the horizontal surface of the frozen pond, its acceleration is given by:

The distance that an accelerating object travels while decelerating from a speed v to a stop with an acceleration a is:

Replace a=μg as well as v=1.6m/s, g=9.8m/s^2 and μ=0.18:

Therefore, to the nearest hundredth, the distance traveled by the toboggan is 0.73m.

Answer:

.73 m

Explanation:

Kinetic Energy = 1/2  m v^2 =   1/2  * 6  * (1.6)^2 = 7.68 J

The work of friction must equal this for the sled to stop

 Force of friction =   .18  *   6 kg * 9.81 m/s^2 = 10.59 N

     Force * Distance = work

        10.59 * d = 7.68 J

           d = .73 m

Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.  

When materials vibrate, waves are created that travel through the substance, and this energy is what we hear as sound. Earthquakes are earth vibrations that cause the (potential) energy held within rocks to be released (as a result of their pressure-generating relative positions). Seismic waves are produced by earthquakes.

How do sound waves and earthquakes compare?

The waves lose energy as they move through the air with sound or through the ground with shaking during an earthquake. Therefore, a band can be heard louder close to the stage than farther away, and an earthquake can be felt more strongly close to the fault than farther away.

In actuality, sound in the air cannot match how quickly earthquake waves move. In rock, the compressional or "P" wave of an earthquake moves at the In actuality, sound in the air cannot match how quickly earthquake waves move. The speed of a P wave is typically 10,000 mph. The speed of sound through air is roughly 750 mph.

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Answer:

32401

92012

65810

100000

Answer:

-48cm

Explanation:

For a convex lens f is +ve and V is +ve

Using the formula 1/f=1/v+1/u

u=12cm and f=16cm

1/16-1/12=1/v

1/v=-1/48

v=-48cm

The time required for half of the oil droplets to coalesce is 34.65 minutes.b) Calculation to find how long it takes for practically all of the oil droplets to coalesce:To find the time it would take for practically all of the oil droplets to coalesce, we need to use the following formula and solve for time when n is equal to 0.0 = e^(-0.02t)-infinity = -0.02tNo oil droplets remain after an infinite amount of time. Therefore, it takes an infinite amount of time for all the oil droplets to coalesce.Answer: It takes an infinite amount of time for all the oil droplets to coalesce.

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A projectile is an object thrown into the air and subject only to gravity and, if applicable, air resistance. The time taken by disc C to reach its maximum height is approximately 1.53 seconds, and its maximum height above the ground is around 11.48 meters. The time from when disc C was thrown upwards until ball B hits the disc is roughly 1.29 seconds.

3.1 Explanation of the term projectile:

A projectile refers to an object that is launched or thrown into the air and is subject only to the forces of gravity and air resistance (if applicable). The motion of a projectile can be analyzed independently of its mass, shape, or any other physical property. The key characteristic of a projectile is that it follows a curved path known as a trajectory.

When a projectile is launched, it moves along a parabolic trajectory due to the combination of its initial velocity and the force of gravity acting vertically downward. The horizontal motion of a projectile remains constant and unaffected by gravity, while the vertical motion is influenced by the acceleration due to gravity.

The path of a projectile can be described mathematically by considering its initial velocity, angle of projection, and the acceleration due to gravity. Projectile motion finds applications in various fields, such as sports, engineering, and physics, where objects are launched or thrown.

3.2.1 Time taken by disc C to reach its maximum height:

To determine the time taken by disc C to reach its maximum height, we can use the kinematic equation for vertical motion. The equation is:

vf = vi + at

Where:

vf = final velocity (which is zero at the maximum height)

vi = initial velocity

a = acceleration (in this case, acceleration due to gravity, -9.8 m/s²)

t = time

Since the disc is thrown vertically upwards, its initial velocity is 15 m/s. We want to find the time it takes for the disc to reach its maximum height, so we'll use the equation and solve for time (t):

0 = 15 + (-9.8)t

Rearranging the equation, we get:

9.8t = 15

t = 15 / 9.8

Calculating this, we find:

t ≈ 1.53 seconds

Therefore, it takes approximately 1.53 seconds for disc C to reach its maximum height.

3.2.2 Maximum height above the ground reached by disc C:

To determine the maximum height reached by disc C, we can use another kinematic equation for vertical motion:

vf² = vi² + 2ad

Where:

vf = final velocity (which is zero at the maximum height)

vi = initial velocity

a = acceleration (in this case, acceleration due to gravity, -9.8 m/s²)

d = displacement (maximum height)

Since we know the initial velocity (vi) and acceleration (a), we can solve for the displacement (d), which represents the maximum height:

0² = 15² + 2(-9.8)d

Rearranging the equation, we get:

0 = 225 - 19.6d

19.6d = 225

d = 225 / 19.6

Calculating this, we find:

d ≈ 11.48 meters

Therefore, the disc C reaches a maximum height of approximately 11.48 meters above the ground.

Calculating the time from the moment that disc C was thrown upwards until the time ball B hits the disc:

To find the time it takes for ball B to hit disc C, we need to calculate the time it takes for both objects to reach the same height.

Since disc C was thrown upwards from the edge of the roof and ball B was shot vertically upwards from the foot of the building, we need to consider the additional height of the building (30 meters).

The time it takes for disc C to reach the ground is the same as the time it takes for ball B to reach a height of 30 meters above the ground.

Using the kinematic equation for vertical motion, we can calculate the time for ball B:

d = vit + 0.5at²

Where:

d = displacement (30 meters)

vi = initial velocity (40 m/s)

a = acceleration (acceleration due to gravity, -9.8 m/s²)

t = time

30 = 40t + 0.5(-9.8)t²

Rearranging the equation, we get:

4.9t² + 40t - 30 = 0

Solving this quadratic equation, we find:

t ≈ 1.29 seconds or t ≈ -5.82 seconds

Since time cannot be negative in this context, we discard the negative solution.

Therefore, it takes approximately 1.29 seconds from the moment that disc C was thrown upwards until ball B hits the disc.

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