Question

One billiard ball is shot east at 3.0 m/s. A second, identical billiard ball is shot west at 0.8 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90° and sending it north at 1.58 m/s. What are the speed and direction of the first ball after the collision?
___________ m/s, ___________   ° south of east

Answer 1

Applying conservation of momentum in the x-direction

Initial momentum = Final momentum

Since the second ball is deflected final velocity in x- direction of second ball is zero, let the velcoity of first ball be v_x

m(+3) + m(-0.8) = mv_x + m(0)

2.2m = mv_x

v_x = 2.2m/s

Applying conservation of momentum in the y-direction

Initial momentum = Final momentum

Since the second ball is deflected final velocity in y- direction of second ball is1.58 m/s, let the velcoity of first ball be v_y

Initial momentum = Final momentum

m(0) + m(0) = mv_y + m(1.58)

0 = mv_y + m1.58

v_y = -1.58 m/s

The magnitude of velocity of first ball is

The angle made by the velocity with the x-axis is

so the velocity of the first ball is 35.7^o south of east