Physics please if anyone can help

Question

Mr. Herbert recorded the total flight time to be exactly 6.5 seconds using your knowledge of physics find out the following about the rocket :

A) the max height

B) find the initial velocity

C) Find the final velocity of the rocket before it hit the ground

Answer 1

This is a 1 dimensional free-fall / projectile motion question.

A) Model the second half (t=3.25 to t=6.5) of the rocket's path from it's max height to the ground:

Max height = -Δh = -(1/2)gt² = -(1/2)*(-10 m/s²)*(3.25 s)² = 52.8 meters

B) Model both halves (t=0 to t=6.5) of the rocket's path from its initial launch to hitting the ground:

Δh = (1/2)gt² + v_ot = 0

Solve for v_o:

v_o = (-(1/2)gt²)/t = -(1/2)gt = -(1/2)*(-10 m/s)*(6.5 s) = + 32.5 m/s

C) Model the second half of the rocket's path (t=3.25 to t=6.5). We should see that v_o = - v_{f .}

v_f = v_o + gt , where v_o = 0 because it's at the top of its path.

v_f = gt = (-10 m/s)*(3.25 s) = - 32.5 m/s

To double-check that our answer is correct, let's use conservation of energy:

∑E_i = ∑E_f

U_i = K_f

mgh_max = (1/2)mv_f²

h_max = v_f² / 2g = (32.5 m/s)² / 2(10 m/s) = 52.8 meters.