Question

You launch a model rocket from ground level. It moves directly upward with a constant acceleration of 73.0 m/s² for 1.35 seconds, at which point it runs out of fuel. Assuming air resistance on the rocket is negligible, what is the maximum altitude (above the ground) achieved by the rocket?
m

Answer 1

Gravitational acceleration = g = -9.81 m/s²

Initial velocity of the rocket = V₁ = 0 m/s

Initial upward acceleration of the rocket = a₁ = 73 m/s²

Time period taken for the fuel to run out = T₁ = 1.35 sec

Velocity of the rocket when the fuel runs out = V₂

V₂ = V₁ + a₁T₁

V₂ = 0 + (73)(1.35)

V₂ = 98.55 m/s

Distance traveled by the rocket before running out of fuel = H₁

H₁ = V₁T₁ + a₁T₁²/2

H₁ = (0)(1.35) + (73)(1.35)²/2

H₁ = 66.52 m

Velocity of the rocket at maximum altitude = V₃ = 0 m/s

Acceleration of the rocket after the fuel runs out = a₂ = g = -9.81 m/s² (Negative as it is directed downwards)

Distance the rocket travels after the fuel runs out till reaching maximum altitude = H₂

V₃² = V₂² + 2a₂H₂

(0)² = (98.55)² + 2(-9.81)H₂

H₂ = 495.01 m

Maximum altitude reached by the rocket = H

H = H₁ + H₂

H = 66.52 + 495.01

H = 561.53 m

Maximum altitude achieved by the rocket = 561.53 m