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?

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