A tennis ball is thrown straight up with an initial speed of 10 m/s. How high does the ball rise?

Question

I need help and the answer on this physics problem.

Answer 1

The vertical motion of a projectile, the tennis ball, is always modeled using the function h(t) = (-1/2)gt² + v₀t +h₀, where g is the constant acceleration of gravity (either 32 ft/s² or 9.8 m/s²), v₀ is the initial velocity, and h₀ is the initial height.

 

Since the velocity is in meters per second, we'll use 9.8 for g.  v₀ would be 10, and h₀ would be 0 since no initial height is indicated.

 

h(t) = (-1/2)(9.8)t² + 10t + 0 = -4.9t² + 10t.

 

The maximum height will happen at the vertex of the parabola.  Using the -b/2a formula, you find the time of maximum height is -10/2(-4.9) = -10/-9.8 ≈ 1.02 seconds.

 

The maximum height would be h(1.02) = -4.9(1.02)² +10(1.02) = 5.1 meters.