3 A crate of mass 45 kg is sliding with a speed of \(0.8 \mathrm {~ms} ^ { - 1 }\) in a straight line across a smooth horizontal floor. One end of a light inextensible rope is attached to the crate. At a certain instant a builder takes the other end of the rope and starts to pull, applying a constant force of 80 N for 5 seconds. While the builder is pulling the crate, the rope makes a constant angle of \(40 ^ { \circ }\) above the horizontal. Both the rope and the velocity of the crate lie in the same vertical plane (see diagram).
\includegraphics[max width=\textwidth, alt={}, center]{b190b8c9-75b0-4ede-913f-cdecdb58180f-3_250_817_605_246} It may be assumed that there is no resistance to the motion of the crate.

1. Determine the work done by the builder in pulling the crate.
2. 1. Find the kinetic energy of the crate at the instant when the builder stops pulling the crate.
   2. Explain why the answers to part (a) and part (b)(i) are not equal.
3. Find the average power developed by the builder in pulling the crate.
4. Calculate the total impulse exerted on the crate by the builder.