Question

A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 53.9m/s2 . The acceleration period lasts for time 10.0s until the fuel is exhausted. After that, the rocket is in free fall. Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s2 .

Answer 1

@rohitmathew

You are not quite correct in your answer above.

The acceleration does not become zero in this case,

The initial 'rocket' phase has an upwards acceleration for 10s. The initial velocity is 0 so you can use v=u+at to work out the final velocity when the rocket stops.

The rocket then continues upwards but decelertating under gravity.

Its maximum height will be when it VELOCITY is 0 (The acceleration is still g)

so use

v^2 = u^2 + 2 as

to find th edistance travelled upwards when it reaches zero velocity.

Answer 2

note - you ALSO have to use

s=ut + 0.5 at^2
to find the height gained during the powered part of the trajectory

Answer 3

no you haven't

The acceleration (after the rocket stops) is always g in the direction downwards.

This cause the upwards velocity to reduce. When the velocity is zero the rocket has reached its maximum height.

(After that - although it is not relevant to this question the velocity increase in a downwards direction, accelerating at a value of g until it hits the ground)

The acceleration never changes, and never becomes 0 (until the rocket hits the ground)

Answer 4

quote
"g is always present.. at the top most point the a=0 g=-9.8 m/s^2
hope i made my point clear"

a=0 is not correct

acceleration = g
velocity = 0

Answer 5

okayy thank u for making it clear.. but what would be the deceleration of the rocket say a few seconds before its final velocity becomes 0?

Answer 6

@MrNood

Answer 7

after the engine stops the acceleration is constant g = 9.81m/s

just be careful of sign (direction) (velocity is upwards at this point, acceleration is downwards)

Why do you ask this? the acceleration is not dependant on the velocity - it is constant