A load is pulled along a horizontal straight track, from $A$ to $B$, by a force of magnitude $P{\text{ }}N$ which acts at an angle of ${30^ \circ }$ upwards from the horizontal. The distance $AB$ is $80{\text{ }}m$. The speed of the load is constant and equal to $1.2{\text{ }}m{\text{ }}{s^{ - 1}}$ as it moves from $A$ to the mid-point $M$ of $AB$.

a) For the motion from $A$ to $M$ the value of $P$ is $25$. Calculate the work done by the force as the load moves from $A$ to $M$.

The speed of the load increases from $1.2{\text{ }}m{\text{ }}{s^{ - 1}}$ as it moves from $M$ towards $B$. For the motion from $M$ to $B$ the value of $P$ is $50$ and the work done against resistance is the same as that for the motion from $A$ to $M$. The mass of the load is $35{\text{ }}kg$.

b) Find the gain in kinetic energy of the load as it moves from $M$ to $B$ and hence find the speed with which it reaches $B$.