A tennis ball is thrown vertically upward with an initial velocity of 8.0 m/s.

a) what will the ball's speed be when it returns to its starting point.
b) how long will the ball take to reach it's starting point?

Let's solve the given problem step-by-step:

a) To find the ball's speed when it returns to its starting point, we need to determine how high it goes. Since the ball is thrown vertically upwards, it will reach its maximum height when its final velocity is zero.

Using the kinematic equation for vertical motion:

vf^2 = vi^2 + 2ad

Where:
vf = final velocity (which is 0 m/s at the maximum height)
vi = initial velocity (8.0 m/s)
a = acceleration (which is equal to -9.8 m/s^2 since it is acting opposite to the direction of motion)
d = displacement

Rearranging the formula, we get:

d = (vf^2 - vi^2) / (2a)

Substituting the given values, we can calculate the maximum height:

d = (0^2 - 8.0^2) / (2 * -9.8)
d = (-64) / (-19.6)
d ≈ 3.27 m

So, the ball reaches a maximum height of approximately 3.27 meters. When it returns to its starting point, it will have the same magnitude of velocity as it did when it was initially thrown upwards.

Thus, the ball's speed when it returns to its starting point is 8.0 m/s.

b) To find the time taken by the ball to reach its starting point, we need to use the concept of symmetry. The time taken to reach the maximum height is equal to the time taken to return to the starting point.

Using the formula for the time taken in vertical motion:

t = (vf - vi) / a

Where:
vf = final velocity (0 m/s at the maximum height)
vi = initial velocity (8.0 m/s)
a = acceleration (-9.8 m/s^2)

Substituting the given values, we can calculate the time taken:

t = (0 - 8.0) / (-9.8)
t = -8.0 / -9.8
t ≈ 0.82 s

So, the ball will take approximately 0.82 seconds to reach its starting point.

To answer these questions, we need to apply the laws of motion and use the given information. Let's break it down step-by-step:

a) What will the ball's speed be when it returns to its starting point?
When a ball is thrown vertically upward, it will reach a maximum height and then fall back down due to gravity. At the highest point, its speed will momentarily reach 0 m/s. However, as it falls back down, it will regain speed.

To determine the ball's speed when it returns to its starting point, we need to consider that the initial velocity is 8.0 m/s and it will move upwards until it reaches its maximum height, where its speed is momentarily 0 m/s.

To calculate the speed when it returns to its starting point, we need to use the concept of conservation of energy. At the starting point, the ball has potential energy due to its height above the ground, and when it returns to its starting point, all of that potential energy is converted into kinetic energy.

The potential energy can be given by the equation:

Potential Energy = m * g * h

where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2), and h is the maximum height reached by the ball.

Since we are dealing with a tennis ball, which has a relatively small mass compared to other objects, we can assume its mass is negligible.

Therefore, the potential energy equation simplifies to:

Potential Energy = m * g * h ≈ 0 (since m ≈ 0)

At the starting point, the potential energy is zero because the height (h) is zero. Therefore, the kinetic energy at the starting point is equal to the total mechanical energy at the highest point.

Kinetic Energy = Potential Energy (at the highest point)

Using the equation for kinetic energy:

Kinetic Energy = (1/2) * m * v^2

where v is the velocity of the ball at the highest point.

Setting the potential energy equal to the kinetic energy:

(1/2) * m * v^2 = 0

Simplifying, we find:

v^2 = 0

This means that the velocity (speed) of the ball when it returns to its starting point will also be 0 m/s. In other words, when the ball reaches the same height it was thrown from, it will momentarily come to a stop before falling back down.

b) How long will the ball take to reach its starting point?
Since the ball is being thrown vertically upward, its motion can be described by the equation:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

At the highest point, the final velocity will be 0 m/s, and the acceleration is the acceleration due to gravity (g = 9.8 m/s^2) acting in the opposite direction (negative).

Therefore,

0 = 8.0 - 9.8 * t

Simplifying, we find:

t = 8.0 / 9.8

Calculating this gives us:

t ≈ 0.82 seconds

Therefore, the ball will take approximately 0.82 seconds to reach its starting point.

Sorry, I don't know, ask someone else