Problem 9.56 Part A Two billiard balls of equal mass move at right angles and me

Question

Problem 9.56 Part A Two billiard balls of equal mass move at right angles and meet at the origin of an ry coordinate system. Initially ball A is moving upward along the y axis at 2.0m/s, and ball B is moving to the right along the z axis with speed 3.7m/s. After the collision (assumed elastic), the second ball is moving along the positive y axis. (Figure 1) What is the final direction of ball A? Express your answer using two significant figures. ? o from the + axis Submit My Answers Give Up Part B What are the speeds of the two balls? Enter your answers numerically separated by a comma. Express your answers using two significant figures. Figure 1 of! ty A" B m/s Submit My Answers Give Up UB = 3.7 m /s A-2.0 m/s

Explanation / Answer

finall 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 slong x axis

3.7m= m vx
3.7= vx----------2

conserving KE

3.7^2 + 2^2= v1^2 + vx^2 + vy^2

4=v1^2 + vy^2-----------3 (put vx=3.7)
using 1 and 3

4= (2-vy)^2 +vy^2
4=4-4vy+2vy^2
2vy=vy^2
vy=2 or vy=0

but vy cannot be 2 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 using (1)
so ball A's final velocity = 3.7m/s along +X axis
and ball B's = 2 m/s along +y axis

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