Question

One billiard ball is shot east at 3.0 m/s. A second, identical billiard ball is shot...

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

Homework Answers

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 vx

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

2.2m = mvx

vx = 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 vy

Initial momentum = Final momentum

m(0) + m(0) = mvy + m(1.58)

0 = mvy + m1.58

vy = -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 35.7o south of east

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