Question

A billiard ball moving at 2.2 m/s strikes a second billard ball at rest and continues at 45 degrees from its original direction, while the other moves at -45 degrees from the same original direction. Both billiard balls have the same mass. Find the speed of the second billiard ball.

1.6 m/s, 3.1 m/s, 0.78 m/s, or 1.1 ,/s

**not sure! thank you!

Answer 1

can we make a diagram of the situation

Answer 2

ok, i am not quite sure how!

Answer 3

yes:) what do we do from here?

Answer 4

note that the collision is not 'head on' , thats why it goes off an angle

Answer 5

yes:) so in calculating, would it be moving at the speed of 3.1 m/s?

Answer 6

ok! what do i plug in for m? :/

Answer 7

momentum = mass *velocity

In elastic collisions, momentum is conserved, therefore "initial momentum = final momentum" . Also kinetic energy is conserved.

initial x momentum = 2.2*m + 0*m
initial y momentum = 0*m + 0*m

final x momentum = m(vf1 cos 45) + m*vf2 cos(-45)
final y momentum = m (vf1 sin 45)+ m (vf2 sin(-45))


2.2 m = m*vf1 cos 45 + m*vf2 cos(-45)
0 = m (vf1 sin 45)+ m (vf2 sin(-45))
1/2m*2.2^2 = 1/2 m* vf1^2 + 1/2* m*vf2^2

Answer 8

we get a system of three equations, (we can cancel m out)

Answer 9

okay! and so we get left with vf1 and vf2? we are looking for vf2 becuase of the second billiard\?

Answer 10

right

Answer 11

how can i solve that value?

Answer 12

momentum = mass *velocity
In elastic collisions, momentum is conserved, therefore "initial momentum = final momentum" . Also kinetic energy is conserved.
initial x momentum = 2.2*m
initial y momentum = 0
final x momentum = m(vf1 cos 45) + m*vf2 cos(-45)
final y momentum = m (vf1 sin 45)+ m (vf2 sin(-45))

2.2 m = m*vf1 cos 45 + m*vf2 cos(-45)
0 = m (vf1 sin 45)+ m (vf2 sin(-45))
1/2m*2.2^2 = 1/2 m* vf1^2 + 1/2* m*vf2^2



canceling out mass m

2.2 = vf1 cos 45 +vf2 cos(-45)
0 = (vf1 sin 45)+ (vf2 sin(-45))
1/2*2.2^2 = 1/2 vf1^2 + 1/2*vf2^2


from the second equation
vf1 sin45 = vf2 sin(45)

vf1 = vf2

Answer 13

now plug that into the first equation

Answer 14

ohh okay ...ermm i got 0.7071 :/ that doesn't look right though L:/

Answer 15

2.2 = vf1 cos 45 +vf2 cos(-45)

vf1 = vf2

2.2 = vf1 cos 45 +vf1 cos(45) because cos(-45) = cos(45)
2.2 = 2vf1 * cos(45)

2.2 /( 2 cos45) = vf1

Answer 16

ohhh okay 1.555 so our solution is 1.6 m/s ?

Answer 17

yes, approximately

Answer 18

to the tenth place , or 2 sig figs

Answer 19

yay! thanks so much!

Answer 20

so it turns out that the speed is the same for both balls after the collision.
this is because they are both the same mass and diverge at symmetric angles

Answer 21

:)