A clinometer is measuring the height of an elevator as it ascends. The clinometer is positioned $10\text{m}$ away from the elevator.

The elevator ascends at a constant speed of $2{\text{ms}}^{-1}.$ The angle of the clinometer is $\theta .$

1. Find an expression for the rate of change of the angle of the clinometer in terms of $\theta .$

2. How quickly is the angle changing when the elevator is $5\text{m}$ off the ground?

In order to get the exact form, don't use $\arctan$ - rather, recall that

In simplest terms, the solution is

Give $p+q$