Question

Two balls of equal mass are projected upwards simultaneously, one from the ground with initial velocity $50m{s}^{-1}$ and the other from a 40 m tower with initial velocity of $30m{s}^{-1}$. The maximum height attained by their centre of mass will be:

• A. $80m$
• B. $60m$
• C. $100m$
• D. $120m$

Answer 1

Answer: (C)

$100m$

Initially the center of mass, COM, will be at a height of 20 m from the ground. Since both are of same mass and are at a distance of 40 m from each other.
The speed of COM will be $\frac{50+30}{2}=40m/s$
$\therefore$ the maximum height reached by the COM is
$20+\frac{{u_c}^2}{2g}=20+\frac{40\times 40}{2\times 10}=100m$
Option C.