physics
A cue ball initially moving at 2.6 m/s strikes a stationary eight ball of the same size and mass. After the collision, the cue ball’s ﬁnal speed is 1.3 m/s.Find the cue ball’s angle θ with respect to its original line of motion. Consider this to be an elastic collision (ignoring friction and rotational motion). Answer in units of ◦

initial x momentum = 2.6 m
initial y momentum = 0
final x momentum = 1.3 m cos T + V m cos A
final y momentum = 1.3 m sin T + V m sin A
T is theta, the cue ball angle from x and A is the 8 ball angle from x
now right off we know that the initial y momentum was zero so the final y momentum is zero
so
1.3 sin T =  V sin A
now what about conservation of energy to get V, the 8 ball speed
(1/2)m(2.6^2)=(1/2)m (1.3^2)+(1/2)m V^2
so
V^2 = 2.6^2  1.3^2
V = 2.25 m/s
so now we know
1.3 sin T =  2.25 sin A
now the x momentum before and after
2.6 = 1.3 cos T + 2.25 cos A
well, we have two equations and two unknown but we would prefer to have all sines or all cosines so square that equation with the sines
1.69 sin^2 T = 5.06 sin^2 A remember A goes  y if T goes + y because we just lost the minus sign :)
so
1.69 (1  cos^2 T) = 5.06(1  cos^2 A)
5.06 cos^2 A = 3.37 + 1.69 cos^2 T
cos^2 A = .666 + .334 cos^2T
cos A = (.666 + .334 cos^2T)^.5
the x momentum equation was
2.6 = 1.3 cos T + 2.25 cos A
so
2.6=1.3cosT+2.25*(.666 +.334 cos^2T)^.5
(.666 +.334 cos^2T)^.5 =(2.61.3cosT)/2.25
so
.666+.334 cos^2T =(1/5.06)(6.766.76cosT +1.69 cos^2 T)
let cos T = p
.666 + .334 p^2 = (1/5.06)(6.766.76p +1.69 p^2
.666 +.334 p^2 = 1.34 1.34 p +.334 p^2
.674 = 1.34 p
p = .503 = cos T
so
T = 59.8 degreesposted by Damon
Respond to this Question
Similar Questions

college physics
A cue ball initially moving at 4.3m/s strikes a stationary eight ball of the same size and mass. After the collision, the cue ball’s final speed is 2.3 m/s at angle 1 with respect to it's original line of motion. The 8 ball 
Physics Part 1
Rick is playing billiards and hits the cue ball. It makes contact with the 8 ball head on. If before the collision the cue ball was travelling at 2.4 m/s and after the collision the 8 ball was traveling at 2.13 m/s. How fast and 
Physics Momentum
A 170g cue ball is moving at 3.0 m/s when it strikes a 160g stationary numbered ball (object ball). After the collision the balls move off as shown. Determine the speed of the cue ball and the numbered (object) ball after the 
Impulse and Momentum
In the game of billiards, all the balls have approximately the same mass, about 0.20 kg. The cue ball moving west with a speed of 4.5m/s strikes another ball at rest. After the collision the cue ball moves at an angle of 55degree 
physics
In a game of pool, the cue ball strikes another ball of the same mass and initially at rest. After the collision, the cue ball moves at 3.10 m/s along a line making an angle of 27.0° with its original direction of motion, and the 
Physics
A cue ball traveling at 0.70 m/s hits a stationary 8ball, which moves off with a speed of 0.23 m/s at an angle of 39° relative to the cue ball's initial direction. Assuming that the balls have equal masses and the collision is 
Physics
A cue ball traveling at 4.0 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30° with its original direction of travel. (a) 
Physics HELP HELP
A cue ball traveling at 4.0 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30° with its original direction of travel. (a) 
physics
In a game of pool, the cue ball strikes another ball initially at rest. After the collision, the cue ball moves at 4.15 m/s along a line making an angle of 25° (i.e. below the xaxis) with its original direction of motion (the 
science
A cue ball traveling at 4.0 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30° with its original direction of travel. (a)