Answer:
a)
b)
Explanation:
Given:
- mass of rocket,
- mass of fuel,
- acceleration of the rocket consuming fuel,
- time after which the fuel exhaust,
<u>During the phase of fuel exhaustion:</u>
<u>velocity attained by the rocket just as the fuel ends:</u>
where:
initial velocity of the rocket = 0
this will be the initial velocity for the phase of ascending of the rocket's height under the influence of gravity.
<u>height at which the fuel finishes:</u>
<u>During the phase of ascend in height of rocket after the fuel is over:</u>
<u>Time taken to reach the top height after the fuel is over:</u>
at top v = (final velocity during this course of motion )= 0
<u>Height ascended by the rocket after the fuel is over:</u>
at the top height the velocity is zero
(-ve sign denotes that the direction of motion is opposite to that of acceleration)
<u>Therefore the maximum altitude attained by the rocket:</u>
b)
time taken by the rocket to fall back to the earth:
where:
initial velocity of the rocket during the course of free fall from the top height.
Now the total time for which the rocket is in the air: