Object at rest slides down a hill of 15°, starts from 100ft above ground. How long does it take to slide down and what speed will it have?

Question

I'll post my question here and then show my incorrect working out.

Suppose that an object starts from rest and slides down a hill whose inclination is 15°. The object slides from a height of 100 feet above the horizontal ground to the ground. How long does it take to slide down the hill and what velocity does the object acquire?

$$s=-16\sin(15^{\circ})t^2+100$$

$$\frac{100}{16\sin(15^{\circ})}=t^2$$

$$t=4.9 \text{ seconds}$$

This is incorrect however, what am I missing?

Answer 1

You did not define whether $s$ is measured across the slope or vertically. If it is measured along the slope the box has to travel $\frac {100}{\sin 15^\circ}$ feet in total at an acceleration of $g \sin 15^\circ$. If you measure it vertically, the acceleration is $g \sin^2 15^\circ$ where one factor of $\sin$ is from the slope reducing the acceleration along the slope and the second is from projecting motion along the slope on the vertical. In either case you are missing one factor of $\sin 15^\circ$