Question

A 25kg rocket stays on a launch pad at rest when it's engines fire and a constant thrust pushes the rocket upward with a constant 500N thrust force. The engines fire for the first 20 m and then abruptly cut off. The maximum height of the rocket is 35m. How much energy does air resistance take away from the rocket?

Answer 1

a = acceleration of rocket for first 20 m = F/m = 500/25 = 20 m/s²

d = distance travelled = 20 m

V_i = initial speed = 0 m/s

V_f = final speed

using the equation

Vf² = Vi² + 2 a d

Vf² = 02 + 2 (20) (20)

V_f = 28.3 m/s

h_i = height at which rocket cut off = 20 m

h_f = maximum height = 35 m

W = work done air resistance

using conservation of energy

KE at h_i + PE at h_i = PE at h_f + W

(0.5) m v_i² + mg h_i = mg h_f + W

(0.5) (25) (28.3)² + (25) (9.8) (20) = (25) (9.8) (35) + W

W = 6336.12 J