A rocket rises vertically, from rest, with an acceleration of 3.2 m/s2 until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity, downward. (a) What is the velocity of the rocket when it runs out of fuel? (b) How long does it take to reach this point? (c) What maximum altitude does the rocket reach? (d) How much lime (total) does it take to reach maximum altitude? (e) With what velocity does the rocket strike the Earth? (f) How long (total) is it in the air?

Solution 75 GP

Step 1 of 7:

In this question, we need to find the velocity of the rocket when it’s fuel runs out

In part b, we need to find the time taken by the rocket

In part c, we need to find the maximum altitude reached by the rocket

In part d, we need to time taken by the rocket to reach maximum altitude

In part e, we need to find the velocity with which the rocket will strike the Earth

In part f, we need to find time rocket remains in air

Data given

Acceleration of the rocket

Height reached by the rocket

Part a:

Step 2 of 7:

We need to find the velocity of the rocket when it’s fuel runs out

Here we understand that the rocket would have reached velocity before it runs out of fuel and the maximum height reached by it will be

That is we need to find the velocity at

We can find the vertical velocity using relation

Substituting values we get

Hence we have velocity of the rocket when it’s fuel runs out as

Part b:

Step 3 of 7:

We need to find the time taken by the rocket

That is we need to find the time taken by the rocket to reach height

It is given by using relation

Rearranging to find time

Substitute and

We get

Hence we have the time taken by the rocket to reach as

Part c: