Two billiard balls of equal mass were moving at right angles when they collided.
ID: 1413550 • Letter: T
Question
Two billiard balls of equal mass were moving at right angles when they collided.Initially ball A had velocity and ball B had velocity .After the elastic collision, ball B moved off in the direction.
Determine the final direction of ball A.
Determine the final speeds of each ball.
10. Two billiard balls of equal mass were moving at right angles when they collided. Initially ball A had velocity vd = (20/) and ball Bhad velocit 1,3(3.7) After . the elastic collision, ball B moved off in the tj direction. Determine the final direction of ball A. Determine the final speeds of each ball. a. b.Explanation / Answer
Initial Momentum along X-axis = -3.7m N-s [-ve indicating the direction is towards Origin]
Initial Momentum along Y-axis = 2m N-s
Let the velocity of the ball A & B are v1 & v2 m/s respectively and A make an angle from the -X-axis :-
By the law of momentum conservation for both axis:-
X-axis:-
mv1cos = -3.7m
v1cos = -3.7 ----------------------(i)
Y-axis:-
mv2 + mv1sin = 2m
v2 + v1sin = 2
v1sin = 2 - v2 ----------------(ii)
as the collision was elastic :-
v1^2 + v2^2 = (2)^2 + (3.7)^2
v1^2 + v2^2 = 17.69 -----------(iii)
By (i)^2 + (ii) ^2:-
v1^2 + v2^2 = (3.7)^2 + 4 + v2^2 - 4v2
17.69 = 13.69 + 4 + v2^2 - 4v2
v2(v2 - 4) = 0
v2 = 4 m/s
By putting this value in (ii):-
v1sin = -2
By (i)^2 + (ii)^2 :-
v1 = 17.29
v1 = 4.16 m/s
By (ii)/(i) :-
tan = 2/3.7 = tan(0.5405)
= 28.4 degree.