Question

A truck is moving with a constant velocity of 54 $km{h}^{-1}$ In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of 20 $m{s}^{-1}$, from the floor of truck, so as to appear at right angles to the truck, for a person standing on earth?

Answer 1

According to LAW STATED BY KEPLER.

$T^2\alpha R^3$

It is know as Law of periods.

Let us consider a plant $P$ of mass $m$ moving with a velocity $v$ around the sun of mass $M$ in a circular orbit of radius $r$

The gravitational force of attraction of the sun on the planet is,

$F=GMm/r^2$

The centripetal force is $F=m{v}^2/r$

equating the two forces,

$m{v}^2/r=GM/r....,\left(i\right)$

If $T$ be the period of revolution of the planet , then

$v=2\pi r/T....,\left(ii\right)$

Substituting $\left(ii\right)$ in $\left(i\right)$

$4{\pi }^2{r}^2/T^2=GM/r$

$r^2/T^2=GM/4p{i}^2$

$M=4{\pi }^2{r}^3/GT$