momentum problem please help?

Question

a ball moving at 5m/s strikes a stationary ball of the same mass
the first ball moves at an angle of 30 degrees relative to th origional line of motion
the second ball moves at an angle of 90 degrees with respect to the final path of the first ball
find the velocity (magnitude and direction) of the second ball after contact
is this elastic or inelastic
explain and show work plz

i get 4.33 and 2.5 which i know is wrong please help me

i get 4.33 and 2.5 which i know is wrong please help me

wow thats what i got and i thought i was probally wrong since i am not the smartest person in the world
thanks

Answer 1

This is elastic since the balls do not stick together. Momentum and energy are therefore conserved.

Initial momentum Pix = mv1, Piy = 0

Where the x and y refer to the momentum in the x and y directions respectively, and v1 is the speed the first ball has before the collision.

Now after the collision ball 2 moves off with velocity:

v3x = v3*cos(30), v3y = v3*sin(30)

Ball 1 moves off at an angle of 30 -90 = -60 degrees relative to the line of original motion. This gives ball 1 a momentum in y that can cancel the y momentum of ball 2. So teh final momentum is

Pfx = mv2cos(-60) +mv3cos(30) remember cos(-x) = cos(x)

Pfy = mv2sin(-60)+mv3sin(30)

Now Piy = 0 = Pfy = mv2 sin(-60) +mv3sin(30)

v2sin(60) = v3 sin(30) ---> sqrt(3) v2/2 =1/2v3 or

v3 = sqrt(3)*v2

Then Pix = Piy

mv1 = mv2cos(-60) +mv3cos(30)

v1 = v2/2 + sqrt(3)*v2 *sqrt(3)/2 = 2 v2

v2 = v1/2 = 2.5 m/s

v3 = sqrt(3)*v2 =4.33