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

a. The same speed, downward.

b. hf=hi+vi*time - 1/2 g time^2
hf, hi are the same: zero. Find time.

a.) -8.0m/s

b.)1.63s

A tennis ball is thrown vertically upward with

an initial velocity of +7.3 m/s.
What will the ball’s velocity be when it
returns to its starting point?

answer is -7.3 m/s

hihiihh

a. When the tennis ball returns to its starting point, its speed will be the same as its initial velocity since it's just reversing direction. So, the speed will be +8.0 m/s.

b. Hmm, do you really want to know how long it will take for the ball to reach its starting point? I mean, technically, it will take forever, because gravity will keep pulling it down and it will keep going up and down in an eternal dance. But if you're asking how long it takes for the ball to reach its highest point and then come back down, that would be a different story. Shall we go with that?

To answer these questions, we need to understand the motion of the tennis ball and apply the principles of projectile motion.

First, let's analyze the ball's motion when it is thrown vertically upward. Since the initial velocity is positive (+8.0 m/s), we know that the ball is moving upward against the force of gravity. The acceleration due to gravity is always directed downward, and its value is approximately 9.8 m/s².

a. What will be the ball's speed when it returns to its starting point?

To determine the ball's speed when it returns to its starting point, we need to consider the ball's vertical motion. As the ball moves upward, it slows down due to gravity until it reaches its highest point, where its velocity becomes zero. Then, on its way back down, it accelerates due to gravity, increasing its speed until it reaches the starting point.

The speed of the ball at its highest point will be zero because it momentarily comes to a stop before changing direction. However, the ball's speed when it returns to its starting point will be the same as its initial speed of +8.0 m/s. This is because the ball will undergo symmetrical motion, meaning that its upward motion speed will match its downward motion speed as long as air resistance is neglected.

b. How long will the ball take to reach its starting point?

Since we now know the initial velocity (+8.0 m/s) and the acceleration due to gravity (-9.8 m/s²), we can find the time it takes for the ball to reach its starting point. The key concept here is that the time for the ball to reach its peak height will be equal to the time for it to fall back to its starting point.

Using the kinematic equation for vertical motion:

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, v = 0 m/s, and u = +8.0 m/s.

0 = 8.0 - 9.8t.

Rearranging the equation:

9.8t = 8.0.

t = 8.0 / 9.8.

Using a calculator, t ≈ 0.816 seconds.

Thus, it will take approximately 0.816 seconds for the ball to reach its starting point.