Question

a ball A collides elastically with another ball B initially at rest. A is moving with a velocity of 10m/s at an angle 60' from the line joining the center. select the correct alternative:
a)velocity of ball A after collision is 5 m/s
b)velocity of ball B after collision is 5√3 m/s
c)velocity of ball A after collision is 7.5 m/s
d)velocity of ball B after collision is 5 m/s

Answer 1

x axis from center A to center B

Ball A before
Vx = 10 cos 60 = 5 sqrt 3
Vy = -10 sin 60 = -5
let m = 1 kg
Ke = (1/2)(100) = 50 Joules

Ball B before Vx = 0 and Vy = 0 and Ke = 0

Ball 1 after
Vx1
Vy1
Ke1 =(1/2)(Vx1^2+Vy1^2)

Ball 2 after
Vx2
Vy2 (has no Vy because hit in x direction
Ke2 = (1/2)(Vx2^2)

momentum before = momentum after
Vx = Vx1+Vx2 = 5
Vy = Vy1 = 8.66 = 5 sqrt 3

energy before = energy after
50*2 = (Vx1^2+Vy1^2)+(Vx2^2)
100 = Vx1^2 + 75 + (5-Vx1)^2
100 = Vx1^2 + 75 +25 -10Vx1 + Vx1^2

2 Vx1^2 - 10 Vx1 = 0
Vx1 = 5 or 0
try 0
then Vx2 = 5 ---- that is d)