Question

a 10 kg and 20 kg ball approach each other with velocities 20m persecond and 10m persecond.what are the velocities after collision . if the collision is perfectly elastic.

Answer 1

Let the velocities of 10 kg & 20 kg ball before collision are u1= 20m/s(+X axis) & u2 = -20( - X axis) and after collision v1 & v2 respectively.Than by the principal of momentum conservation: - 
=>m1u1 + m2u2 = m1v1 + m2v2 
=>10 x 20 + 20 x ( -20) = 10 x v1 + 20 x v2 
=>v1 + 2v2 = -20 ---------------------(i) 
Since the collision is perfectly elastic (e = 1) 
=>e = (v2 - v1)/(u1 - u2) = 1 
=>v2 - v1 = 20 - (-20) = 40 ------------------------(ii) 
On adding (i) & (ii): - 
=>3v2 = 20 
=>v2 = 6.67 m/s 
=>v1 = 6.67 - 40 = - 33.33m/s 
=>The 10 kg ball will travel along - X axis with a velocity of 33.33 m/s & the 20 kg ball will travel along + X axis with a velocity of 6.67 m/s.