Question:
A car is going at a speed of $21.6 \mathrm{~km} / \mathrm{hr}$ when it encounters a $12.8 \mathrm{~m}$ long slope of angle $30^{\circ}$. The friction co-efficient between the road and the tyre is $\frac{\sqrt{3}}{2}$. Show that no matter how hard the driver applies the brakes, the car will reach the bottom with a speed greater than $36 \mathrm{~km} / \mathrm{hr}$. Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.
Solution:
