A student estimated based on the video that the ball left my hand

Question

A student estimated based on the video that the ball left my hand 1.62 meters off the ground, and after 0.6 seconds the ball reached the maximum height of 3.25 meters.

Use this information to find an equation for the height, h of the ball, in meters, after t seconds.

Answer 1

h(t) = h₀ + v₀t - (1/2)gt²

 

h₀ = 1.62 m

g = 9.8 m/s²

 

h(t) = 1.62 + v₀t - 4.9t²

 

h_max = h(0.6) = 3.25 m

 

Use this to find v₀

 

3.25 = 1.62 + v₀(0.6) - 4.9(0.6)²

 

v₀ = [3.25 - 1.62 + 4.9(0.6)²]/0.6 m/s ≅ 5.657 m/s

 

h(t) = 1.62 + 5.657t - 4.9t²

 

Test the solution.