Physics Help?

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 = 2.3 m/s , and ball B is moving to the right along the x axis with speed vB = 3.5 m/s . After the collision, assumed elastic, ball B is moving along the positive y axis

 

A.) What is the final direction of ball A?

 

 

B.) What are their two speeds?

Answer 1

(a)

Step 1:

Ball A is moving upwards along y -axis with a velocity of .

Ball B is moving upwards along x -axis with a velocity of .

Draw the coordinate system for the situtaion.

Observe the figure:

Conversation momentum along x -axis:

Substitute .

Conversation momentum along y-axis:

Substitute .

Conservation of kinetic energy:

 Substitute and .

Step 2:

Consider equation (1).

Squaring on each side.

Consider equation (2).

Squaring on each side.

Add equation (4) and (5).

Substitute .

Since cannot be zero then .

Substitute in equation (1).

After collision Ball A moves with a velocity of .

Substitute in equation (2).

After collision Ball B moves with a velocity of .

As , the Ball A moves in the direction of positive x-axis.

Solution:

The Ball A moves in the direction of positive x-axis.

Comments

It needs to be from the y direction. How do you switch it?

Answer 2

(b)

From part (a):

Ball A moves with a velocity of after collision.

Ball B moves with a velocity of after collision.