Question

A ball of mass m makes a head-on elastic collision with a second ball (at rest) and rebounds with a speed equal to 0.370 its original speed. What is the mass of the second ball?

Answer 1

let

let m1 = m is the mass of the first ball.

let m2 is the mass of the second ball.

let u1 is the initial velocity of the first ball.

v1 = -0.37*u1 is the velocity of the first ball after the collision.

u2 = 0 (initial velocity of second ball)

we know,

velocity of the first ball after the collsion,

v1 = (m1 - m2)*u1/(m1 + m2)

-0.37*u1 = (m1 - m2)*u1/(m1 + m2)

-0.37*(m1 + m2) = m1 - m2

-0.37*m1 - 0.37*m2 = m1 - m2

m2 - 0.37*m2 = m1 + 0.37*m1

m2*(1 - 0.37) = 1.37*m1

m2 = 1.37*m1/(1-0.37)

= 2.17*m <<<<<<<<<<--------------------Answer