8 In this question use \(g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) A lift is used to raise a crate of mass 250 kg
The lift exerts an upward force of magnitude \(P\) newtons on the crate.
When the crate is at a height of \(x\) metres above its initial position $$P = k ( x + 1 ) ( 12 - x ) + 2450$$ where \(k\) is a constant. The crate is initially at rest, at the point where \(x = 0\)
8

1. Show that the work done by the upward force as the crate rises to a height of 12 metres is given by $$29400 + 360 k$$ 8
2. The speed of the crate is \(3 \mathrm {~ms} ^ { - 1 }\) when it has risen to a height of 12 metres. Find the speed of the crate when it has risen to a height of 15 metres.
   8
3. Find the height of the crate when its speed becomes zero.
   8
4. Air resistance has been ignored.
   Explain why this is reasonable in this context.