Question

Two balls A and B of masses 40g and 50g are moving at speeds of 40m/s and 30m/s respectively. If after colliding a starts moving with a velocity of "20m/s" in opposite direction find the velocity of b

Answer 1

Question :

• Two balls A and B of masses 40g and 50g are moving at speeds of 40m/s and 30m/s respectively. If after colliding a starts moving with a velocity of "20m/s" in opposite direction find the velocity of b

Given :

• mass of ball A(m a).= 40 g =0.04 kg

• mass of ball B (m b)= 50 g = 0.05 kg

• initial velocity of ball A(u a) = 40 m/s

• initial velocity of ball B (u b)= 30 m/s

• final velocity of ball A (v a)= - 20 m/s

Note : negative sign denotes the movement of ball in opposite direction

To find :

• final velocity of ball B

Concept :

As no external force is acting in the system the total momentum of the system is conserved . Hence ,we can apply law of conservation of momentum in order to solve this question

Solution :

By applying law of conservation of momentum ,

$\rightarrow \mathtt {\large{P_i=P_f}}$

$\rightarrow \mathtt {\large{m_au_a +m_bu_b =m_av_a +m_bv_b}}$

$\rightarrow \mathtt {\large{0.04 \times 40 +0.05 \times 30=0.04 \times - 20 +0.05 \times v_b}}$

$\rightarrow \mathtt {\large{1.6+1.5= - 0.8 +0.05 \times v_b}}$

$\rightarrow \mathtt {\large{3.1=0.8+0.05 \times v_b}}$

$\rightarrow \mathtt {\large{3.9=+0.05 \times v_b}}$

$\rightarrow \mathtt {\large{v_b = \dfrac{3.9}{0.05} }}$

$\rightarrow \mathtt {\large{v_b = 78 \dfrac{m}{s} }}$