Question

A rocket is moving away from the solar system at a speed of 7.5 ✕ 103 m/s. It fires its engine, which ejects exhaust with a speed of 5.0 ✕ 103 m/s relative to the rocket. The mass of the rocket at this time is 6.5 ✕ 104 kg, and its acceleration is 4.0 m/s2.

What is the velocity of the exhaust relative to the solar system? (B) At what rate was the exhaust ejected during the firing?

Answer 1

Part a)

`v_E = 2.5 * 10^3 m/s`

Part b)

`(dm)/(dt) = 52 kg/s`

Step-by-step explanation:

Part a)

As we know that the velocity of exhaust with respect to the rocket is given as

`v_(ER) = v_E - v_R`

so we will have

`-5 * 10^3 = v_E - 7.5 * 10^3`

`v_E = 2.5 * 10^3 m/s`

Part b)

As we know that

`F = ma`

here F = thrust force on the rocket

So we have

`v_(ER) (dm)/(dt) = ma`

`(5 * 10^3) (dm)/(dt) = (6.5 * 10^4)(4)`

`(dm)/(dt) = 52 kg/s`