9702_s22_qp_12 Question 10

Two balls X and Y are moving towards each other with speeds of 5 m s^–1 and 15 m s^–1 respectively. 

They make a perfectly elastic head-on collision and ball Y moves to the right with a speed of 7 m s^–1. 

What is the speed and direction of ball X after the collision? 

A 3 m s^–1 to the left 

B 13 m s^–1 to the left 

C 3 m s^–1 to the right 

D 13 m s^–1 to the right

ANSWER: B

The Physics Behind

• In a perfectly elastic collision, 
• the kinetic energy is conserved, and
• the momentum is conserved.
• Combining these two conservation principles in this type of collision reveals that 

u_X - u_Y  =  v_Y - v_X

"the relative speed of approach equals the relative speed of separation"

where u stands for before-collision velocities and v as after-collision velocities

• Using the above equation,

(+5 m s^–1) - (-15 m s^–1) | =  (+7m s^–1) - v_X

20 m s^–1 = 7 m s^–1 - v_X

v_X = - 13 m s^–1

Answer: 27 m s^–1, the negative sign means to the left