A tennis ball is thrown directly upward with an initial speed of 25 m/s.

What is its velocity in m/s when it hits the ground?

is there any reason to think it will be different than the launch velocity?

Vf^2=Vi^2+2ad where d is displacement, and a is -9.8. When at the ground, d is zero.

To find the velocity of the tennis ball when it hits the ground, we need to consider its initial velocity and the acceleration due to gravity.

First, let's assume that the upward direction is positive. The initial velocity of the tennis ball, when thrown directly upward, is 25 m/s. However, when the ball reaches its maximum height, its velocity becomes zero momentarily before starting to fall downward.

The acceleration due to gravity is always acting downward and is approximately 9.8 m/s² (assuming no air resistance). As the ball falls downward, its velocity increases steadily due to the acceleration.

To find the velocity of the ball when it hits the ground, we can use the following equation of motion:

v² = u² + 2as

where:
v is the final velocity (what we want to find)
u is the initial velocity (25 m/s)
a is the acceleration due to gravity (-9.8 m/s², considering downward as negative)
s is the displacement (how far the ball falls, which is the height)

Since the ball is initially thrown upward and then falls back down to the ground, the displacement s is equal to the height it reached. However, since we don't know the height, we cannot directly solve for the final velocity.

However, we can use another equation to find the time it takes for the ball to reach its maximum height. The equation is:

v = u + at

Rearranging the equation, we have:

t = (v - u) / a

Plugging in the values, we get:

t = (0 - 25) / (-9.8)
t = 2.54 seconds (approximately)

Since the ball takes the same amount of time to reach its maximum height as it takes to fall back down, the total time of flight is twice the time calculated:

Total time = 2t = 5.08 seconds (approximately)

Now, we know the total time of flight, and we can use it to calculate the height reached by the ball using the formula:

s = ut + 0.5at²

Plugging in the values, we have:

s = (25)(5.08) + 0.5(-9.8)(5.08)²
s = 126.9 meters (approximately)

So, the height reached by the ball is approximately 126.9 meters.

Finally, we can use the equation of motion to find the final velocity when the ball hits the ground:

v² = u² + 2as

Plugging in the values, we have:

v² = (25)² + 2(-9.8)(-126.9)
v² = 625 + 2481.04
v² = 3106.04

Taking the square root of both sides, we get:

v = √3106.04
v ≈ 55.7 m/s

Therefore, the velocity of the tennis ball when it hits the ground is approximately 55.7 m/s.