Question

A 0.25 kg ball moving at a speed of 3 m/s, along the positive x-axis, strikes a stationary horizontal ball of mass 0.30 kg. (a) If the collision is perfectly inelastic, what is the velocity and direction of the balls? (b) If the second ball moves at a rate of 1 m/s towards the positive x-axis, what is the velocity and direction of the first 2. ball after collision?

Answer 1

Mass of ball m_1 = 0.25 kg initial speed u_1 = 3 m/s mass of ball m_2 = 0.30 kg, u_2 = 0 (a) As collision is perfectly in elastic hence balls will stick together after collision & will continue moving in same direction with speed V therefore using momentum conservation m_1 u_1 + m_2 u_2 = (m_1 + m_2) v 0.25 times 3 + 0.30 times 0 = (0.25 + 0.30) V therefore 0.55 V = 0.75 V = 0.75/0.55 = 1.36 m/s along +ve X axis \r\n (b) id u_1 = 1 m/s then again m_1 u_1 + m_2 u_2 = (m_1 + m_2)v 0.25 times + 0.30 times 1 = (0.25 + 0.30) V therefore 0.55 V = 0.75 + 0.30 = 1.05 V = 1.05/0.55 = 1.91 m/s both the balls will be moving with same speed of 1.91 m/s