Question

If a rocket with a mass of 4000 tons vertically accelerates at a rate of `6/5 m/s^2`, how much power will the rocket have to exert to maintain its acceleration at 11 seconds?

Answer 1

`P = 1.9 × 10^14 W`

Explanation:

First we will calculate the thrust force of the rocket, then we will find the velocity of the rocket at 11 seconds and lastly calculate the power at 11 s required to maintain its acceleration at that velocity.

Thrust force (using simplified version of Newton’s second law):
Mass: m = 4000 tons `= 4000 × 1000 kg = 4.0 × 10^6 kg`
`F = ma = 4.0 × 10^6 × 65 = 2.6 × 10^8 N`

Velocity of the rocket at 11 s:
Use equation of constant acceleration, assuming it starts at rest.
`s = ?`
`u = 0`
`v = ?`
`a = 65 m s^(-2)`
`t = 11 s`

Use `v = u + at = 0 + 65 × 11 = 715 m s^(-1)`

Power exerted at 11 s:
`P = Fv = 2.6 × 10^8 × 715 = 1.859 × 10^14 = 1.9 × 10^14 W` (2 sf)