Question

1)A ball moving at 19 m/s makes an off-center elastic collision with another ball of equal mass that is initially at rest. The incoming ball is deflected at an angle of 50◦ from its original direction of motion. Find the speed of the first ball after the collision. Answer in units of m/s.

2) Find the speed of the second ball. Answer in units of m/s.

Answer 1

From conservation of momentum (m1v1= m2v2), we can see that the initial velocity of the 1st ball is distributed between the 1st and 2nd balls after the collision.

Now since after the collision, the 1st ball is deflected by 50⁰from its original direction, its final velocity is given by,

V_{​​​​​​1f}​​​​ = Vcos = 19*cos(50) = 12.21m/s

Hence, the velocity of the 2nd ball is, from vector addition,

V_{​​​​​​2f}​​​​ = √19² - (12.21)² = 14.55 m/s

∴ the velocity of the 1st ball = 12.21 m/s

and the velocity of the 2nd ball = 14.55m/s