Question

A body is thrown vertically upwards from ground with a speed of $10m/s$. If coefficient of restitution of ground, $e=1/2$. If the total distance travelled by the time it almost stops is $\frac{33+x}{3}m$, find the value of $x$.

Answer 1

Coefficient of restitution , $e=\sqrt{\frac{bounceheight}{dropheight}}$

So here when you throw a ball vertically upwards then the drop height (when ball is coming downwards after reaching top most point) will be $5$

So using the above formula we get that that the bounce height is going to be $\frac{5}{4}$ and this will keep on going till ball comes to stop.

This is making a GP will $r=\frac{1}{4}$ and $a=10$

So total distance covered is $\frac{10}{1-\frac{1}{4}}$ = $\frac{40}{3}$

This gives as $x=7$