Question

A particle is fired vertically upward with a speed of $15km/s$. Find the speed of the particie when it goes out of the earth's gravitational pull.

Answer 1

When the particle moves out of earth's pull, there will be no interaction energy between the particle and the earth. Hence, from energy conservation,

$\frac{1}{2}m{15}^2-\frac{GMm}{R}=\frac{1}{2}m{v}^2$

$225X{10}^6-2\left(9.8\right)\left(6400000\right)=v^2$

$v\approx 9.97km/s$

Answer is $9.97km/s$