Question

Two balls of equal masses are projected upward simultaneously, one from the ground with speed of 50 m/s and other from a 40 m high tower with initial speed of 30 m/s. Find the maximum height attained by their center of mass.

Answer 1

Speed of center of mass $=\frac{m\left(50\right)+30\left(m\right)}{2m}=40m/s$

Initially, their center of mass at height $h_1=20$m above.

Height attaint by com $h_2=\frac{V^2{\sin }^2\theta }{2g}=\frac{40\times 40}{2\times 10}=80m$

Total height attaint by their com prom ground

$h_1+h_2=20+80=100$m