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#

We will compute the rocket's thrust force first, then its velocity at 11 seconds, and finally the power needed at 11 seconds to keep the rocket's acceleration going at that speed.

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)

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elena Albarran

The rocket would have to exert approximately 4800 kilowatts of power to maintain its acceleration at 11 seconds.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.