Question

Two balls A and B of masses 40 gm and 50 gm are moving at speeds of 40 $m/s$, and 30 $m/s$, respectively. If velocity at 25 $m/s$, what is the velocity of A ?

Answer 1

Hint: In order to solve the collision problems, we have to use 2 conservation methods which are –
1. Momentum conservation method
2. Energy conservation method

Complete step by step solution:

Given that before collision -
Velocity of ball $A({V_A}) = 40m/s$
Velocity of ball $B({V_B}) = 30m/s$
Mass of $A({m_A}) = 40gm$
Mass of $B({V_B}) = 50gm$
After collision -
Velocity of ball $A(V_A^1) = ?$
Velocity of ball $B(V_B^1) = 25m/s$
According to the law of conservation of momentum
Total momentum before collision $ = $ Total momentum after collision
${m_A}{V_A} + {m_B}{V_B} = {m_A}v_A^1 + {m_B}V_B^1$
$40 \times 40 + 50 \times 30 = 40 \times V_A^1 + 50 \times 25$
$1600 + 1500 = 40V_A^1 + 1250$
$40V_A^1 = 3100 - 1250$
$V_A^1 = \dfrac{{1850}}{{40}}$
$V_A^1 = 46.45m/s$
Hence, the velocity of ball A after collision is $46.45m/s$

Note: In many problems of collision, we cannot get a final answer only using law of momentum conservation. In that case we have to use the law of energy conservation also. If collision is elastic, then we can also use the law of kinetic energy conservation also.