Question

two perfectly elastic balls A and B of masses 2kg and 4kg respectively move in opposite directions with velocities of 4m/s and 1m/s. find the final velocities of the two balls after collision

Answer 1

v is final velocity of A (to the left) and u is final velocity of B (to the right).

From the conservation of momentum:

$$2(4)-4(1)=-2v+4u$$

$$v=2u-2$$

From the conservation of energy:

$$0.5(2)(4)^2+0.5(4)(1)^2=0.5(2)v^2+0.5(4)u^2$$

$$18=2u^2+v^2$$

So,

$$18=2u^2+(2u-2)^2$$

$$u=\frac{7}{3}\frac{m}{s}$$

$$v=2\frac{7}{3}-2=\frac{8}{3}\frac{m}{s}$$