Two inelastic spheres weighing 8 kg and 2 kg move at speeds of 5 m / s and 3 m / s

Two inelastic spheres weighing 8 kg and 2 kg move at speeds of 5 m / s and 3 m / s, respectively, directed along one straight line in one direction. How fast will they move after an absolutely inelastic collision?

m1 = 8 kilograms – the mass of the first ball;

v1 = 5 m / s – speed of the first ball;

m2 = 2 kilograms – the mass of the second ball;

v2 = 3 m / s – speed of the second ball.

It is required to determine the speed of the balls v (m / s) after an absolutely inelastic impact.

According to the problem statement, the balls move in one direction along one straight line. Also, as a result of inelastic impact, they will move together as a whole. Then, according to the law of conservation of momentum (momentum):

m1 * v1 + m2 * v2 = (m1 + m2) * v;

v = (m1 * v1 + m2 * v2) / (m1 + m2) = (8 * 5 + 2 * 3) / (8 + 2) =

= (40 + 6) / 10 = 46/10 = 4.6 m / s.

Answer: the speed of the balls will be 4.6 m / s.