Question

A 0.280-kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. (A) What is the mass of the second ball?

Answer 1

Answer:

mass of second ball is 0.84 kg

Explanation:

mass of ball = 0.280 kg

to find out

mass of the second ball

solution

we know here elastic head on collision and

second ball moves =  half the original speed

we consider here m1 mass of 1st ball and m2 mass of second ball

v1 = velocity of first ball before collision

v2 = velocity of second ball before collision

v3 = velocity of first ball after collision

v4 = velocity of second ball after collision

so here

we know 2nd ball was on rest so v2 = 0

after collision v4 = 1/2 ( v1)

and we know head on collision so

v3 = - v1/2

so from law of conservation of mass

m1v1 + m2v2 = m1v3 + m2v4

put here value

m1v1 + m2(0) = m1(-v1/2) + m2(v1/2)

solve and we get

m2 = 3m1

m2 = 3( 0.280) = 0.84

mass of second ball is 0.84 kg