question in description

Question

You launched a model rocket with an initial velocity of 16 m/s off a platform that is 19 meters off the ground. what is the max height of the rocket? at what time does the max height occur?

Answer 1

h(t) = -(1/2)gt² + v₀t + h₀, g =9.8 m/s²

 

h(t) = -4.9t² + 16t + 19

 

Under constant acceleration,

 

v(t) = v₀ - gt = 16 - 9.8t

 

Maximum height occurs when v drops to zero and the rocket begins to fall.

 

v = 16 - 9.8t = 0

 

t = 16/9.8 = 1.633 s

 

h_max = -4.9(1.633)² + 16(1.633) + 19 = 32.061 m, at 1.633 s after launch