Another similar one hit the stationary billiard ball. After the impact, the balls scattered at an angle of 90

Another similar one hit the stationary billiard ball. After the impact, the balls scattered at an angle of 90 so that the momentum of one became equal to 0.3 kg * m / s, and the other 0.4 kg * m / s. What momentum did the projected ball have before impact?

Given:

a = 90 degrees – the angle between the scattered balls;

p1 = 0.3 kg * m / s – momentum of the first ball after collision;

p2 = 0.4 kg * m / s – the momentum of the second ball after the collision.

It is required to determine the momentum of the first ball before collision p (kg * m / s).

Since the balls flew away with a certain angle a, then according to the law of conservation of momentum (momentum):

p = p1 * cos (a / 2) + p2 * cos (a / 2) = cos (a / 2) * (p1 + p2) =

cos (90/2) * (0.3 + 0.4) = cos (45) * 0.7 = 0.7 * 0.7 = 0.49 kg * m / s.

Answer: the momentum of the first ball before the collision was 0.49 kg * m / s.