Two billiard balls of equal mass move at right angles and meet at the origin of
ID: 2259324 • Letter: T
Question
Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at vA = 2.3m/s , and ball B is moving to the right along the x axis with speed vB = 4.4m/s . After the collision, assumed elastic, ball B is moving along the positive y axis. A) What is the final direction of ball A? Express your answer using two significant figures. B) What are their two speeds? Express your answers using two significant figures. Enter your answers numerically separated by a comma.Explanation / Answer
let the components of velocity of a be vx and vy along positive x and y axes and let Ball be move with velocity v1 along +ve y axis(given)
conserve momentum along y axis
2m = mv1 + mvy
2= v1+vy----------(1)
conserve along x axis
4.4m= m vx
4.4= vx------------(2)
conserving KE
4.4^2 + 2.3^2= v1^2 + vx^2 + vy^2
5.29=v1^2 + vy^2--------------(3) (put vx=4.4)
using 1 and 3
5.29= (2.3-vy)^2 +vy^2
5.29=5.29-4.6vy+2vy^2
2.3vy=vy^2
vy=2.3 or vy=0
but vy cannot be 2.3 because then v1 would become zero that is ball b comes to rest not possible(given in question ball b moves up after colliding)
so vy=0
v1=2.3 using (1)
so ball A's final velocity = 4.4m/s along +X axis
and ball B's = 2.3 m/s along +y axis