A ball with a mass of m is moving with a speed of 2.2 m/s to the right (which is

Question

A ball with a mass of m is moving with a speed of 2.2 m/s to the right (which is the positive direction) when it collides head on with a stationary ball of mass 3m. If the collision is elastic, what is the speed of the two balls after the collision?

a. The light ball has a speed of -1.1m/s and the heavy ball has a speed of +1.1m/s

b. The light ball has a speed of -1.1m/s and the heavy ball has a speed of +3.3m/s

c. The light ball has a speed of +1.1m/s and the heavy ball has a speed of +3.3m/s

d. The light ball has a speed of +3.3m/s and the heavy ball has a speed of +1.1m/s

e. The light ball has a speed of +1.1m/s and the heavy ball has a speed of +2.2m/s

Please explain!

Explanation / Answer

mass of light ball m

mass of heavy ball 3m

momentum of light ball = m V = 2.2 * m

momentum after collision = mV1+ 3mV2

momentum remains constant therefore

2.2*m = mV1+ 3mV2

V1 +3V2 = 2.2 ............(1)

now go for kinetic energy

since collision is elastic there will be no loss of energy

therefore

1/2 * m V^2 = 1/2 * m (V1^2 + V2^2)

V^2 = (V1^2 +3V2^2 )

4.84= V1^2 +3V2^2     ...........(2)

putting the value of V1 from equation 1 to 2

we get

4.84 = (2.2-3V2)^2 +3V^2

4.84= 4.84 +12 V2^2 -13.2 V2 ..............(3)

Solving equation 3 we get

V2 = 1.1

putting V2 in equation 1 we get

V1 = -1.1

therefore

light ball speed V1 = -1.1 m/s

heavy ball speed V2 = 1.1 m/s

So your option 'a' is correct

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