   Chapter 6, Problem 53P

Chapter
Section
Textbook Problem

A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. Alter the collision, the first ball moves at 4.33 m/s at an angle of 30.0° with respect to the original line of motion, (a) Find the velocity (magnitude and direction) of the second ball after collision, (h) Was the collision inelastic or elastic?

(a)

To determine
The velocity of the second ball after collision.

Explanation

Given info: Velocity of the first ball before collision ( v1 ) is 5.00 m/s. Velocity of the first ball after collision ( v2 ) is 4.33 m/s. The first ball moves at angle of θ=30ο with respect to the original line of motion.

From law of conservation of momentum,

Along the horizontal direction,

mv1=mv2cosθ+mu2cosϕ (I)

• m is the mass of the two balls.
• ϕ is the angle of the second ball with respect to the line of motion.
• u2 is the velocity of the second ball after collision.

Along the vertical direction,

0=mv2sinθ+mu2sinϕ (II)

From Equations (I) and (II),

ϕ=tan1[sinθcosθ(v1v2)]

Substitute 5.00 m/s for v1 , 4.33 m/s for v2 and 30ο for θ .

ϕ=tan1[sin30οcos30ο(5

(b)

To determine
The type of collision.

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