Question

Two spheres A and B moving in opposite directions have velocities of $10m{s}^{-1}$ and $20m{s}^{-1}$. The two spheres collide with each other elastically. If A continues to move in the same direction at $4m{s}^{-1}$, the velocity of sphere B just after the collision is

• A. $34m/s$ in the same direction
• B. $34m/s$ in the opposite direction
• C. $26m/s$ in the same direction
• D. $34m/s$ in the opposit direction

Answer 1

Answer: (A)

$34m/s$ in the same direction

Given,

$u_A=10m/s$

$u_B=-20m/s$

$v_A=4m/s$

$v_B=?$

The collision is elastically, so the coefficient of restitution is unity.

$e=\frac{v_B-v_A}{u_A-u_B}=1$

$v_B-v_A=u_A-u_B$

$v_B=v_A+u_A-u_B$

$v_B=\left(4m/s\right)+\left(10m/s\right)-(-20m/s)=(4+10+20)m/s$

$v_B=34m/s$ in the same direction.

The correct option is A.