Two balls A and B of equal masses are projected upward simultaneously, one from

Question

Two balls A and B of equal masses are projected upward simultaneously, one from the ground with speed 50

m s^{- 1}

and other from height 40 m above the first ball high tower with initial speed 30

m s^{- 1}

. Find the maximum height attained by their centre of mass.

Options:

A . 80 m

B . 100 m

C . 20 m

D . 60 m

Answer: Option B
:
B
The initial position of centre of mass is

y_{c m} = \frac{m \times 0 + m \times 40}{2 m} = 20 m

Initial velocity of centre of mass

u_{c m} = \frac{m \times 50 + m \times 30}{2 m} = 40 m s^{- 1}

Acceleration of centre of mass,

a_{c m} = - g

Using kinematics equation:

v_{c m}^{2} = u_{c m}^{2} + 2 a_{c m} H

Here H is the maximum height reach by centre of mass of two balls from initial level.

∴

0^{2} = 40^{2} - 2 \times 10 \times H

\Rightarrow H = \frac{1600}{20} = 80 m

Hence, maximum height reach by centre of mass from ground level will be

h_{m a x} = (h_{c m})_{i n i t i a l} + H = 20 + 80 = 100 m

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