This is a problem I discovered on the Yahoo answers physics page: A toy rocket of mass 0.2 kg is projected vertically upwards from rest by means of force which decreases uniformly in 2 seconds from 2 kg wt to zero and thereafter ceases. Find the maximum height reached.
First of all, I was not aware of the fancy kg wt unit. A simple Google search showed that 1 kg wt = 1 N. So we can now begin with a sketch of the problem.
The problem is divided into 2 parts: one with non uniform acceleration (represented by , from t = 0 s to t = 2 s) and the other with uniform deceleration (
, after t = 2 s).
The non-uniform acceleration is given by
After 2 s, the acceleration becomes
The (1D) force at time
can be determined using the conditions prescribed by the problem and recalling that
has a linear profile:
and hence
The velocity of the rocket at t = 2 s is therefore
Also,
We can therefore calculate
This gives m.
Determining is a simple problem with uniform acceleration
This gives m.
Therefore, the maximum height = m.
