denise is a volleyball player she will know the projectile motion of volleyball. the ball has an initial velocity of zero. as she serves the ball it hits the ground after 5.0 seconds, what is the final velocity of the ball before it touch the ground and how tall did she serve the ball

Question

denise is a volleyball player she will know the projectile motion of volleyball. the ball has an initial velocity of zero. as she serves the ball it hits the ground after 5.0 seconds, what is the final velocity of the ball before it touch the ground and how tall did she serve the ball

Answer 1

To find the final velocity of the ball before it touches the ground, we can use the equation for projectile motion:

𝑑 = 𝑣₀𝑡 + (1/2)𝑎𝑡²

In this equation, 𝑑 represents the vertical displacement, 𝑣₀ represents the initial velocity, 𝑡 represents the time it takes for the ball to hit the ground, and 𝑎 represents the acceleration due to gravity (approximately -9.8 m/s²).

We know that the initial velocity (𝑣₀) is zero, which means the first term on the right-hand side of the equation becomes zero. Therefore, the equation simplifies to:

𝑑 = (1/2)𝑎𝑡²

We are given the time (𝑡) as 5.0 seconds. Substituting the value of time, we get:

𝑑 = (1/2)(-9.8 m/s²)(5.0 s)²
= (1/2)(-9.8 m/s²)(25.0 s²)
= -122.5 m

The negative sign indicates that the displacement is downward, as the ball falls towards the ground.

Next, to find out the height at which she served the ball, we need to consider the starting point of the ball. Since the initial velocity is zero, we can assume that the ball was initially at rest on the ground. Hence, the height at which she served the ball would be equal to the displacement, but with the sign flipped:

Height = |𝑑| = 122.5 m

Therefore, the final velocity of the ball before it touches the ground is not applicable in this case since the initial velocity is zero. The height at which Denise served the ball is 122.5 meters.