A cue ball traveling at 4.0 m/s makesa glancing, elastic collision with a target
ID: 1753396 • Letter: A
Question
A cue ball traveling at 4.0 m/s makesa glancing, elastic collision with a target ball of equal mass thatis initially at rest. The cue ball is deflected so that it makes anangle of 30° with its original direction of travel. (a) Find the angle between the velocity vectorsof the two balls after the collision.1°
(b) Find the speed of each ball after the collision. cue ball 2 m/s target ball 3 m/s (a) Find the angle between the velocity vectorsof the two balls after the collision.
1°
(b) Find the speed of each ball after the collision. cue ball 2 m/s target ball 3 m/s cue ball 2 m/s target ball 3 m/s
Explanation / Answer
let u = velocity of cue ball before collision = 4 m/s in the xdirection v = velocity of cue ball after collision at angle 300 tox direction V = velocity of target ball after collision at angle - to xdirection (i.e., below the axis) momentum conservation in the x-direction gives mu = mv cos 300 + mV cos u = v 3/2 + V cos >>> equation A momentum conservation in the y-direction gives 0 = mv sin 300 - mV sin v/2 = V sin >>> equation B KE conservation gives (1/2)mu2 = (1/2)mv2 + (1/2)mV2 u2 = v2 + V2 >>>equation C u2 - v2 = V2 = v2/4 +(u - v3/2)2 = v2/4 + u2 +3v2/4 - uv3 = v2 + u2 -uv3 2v2 = uv3 v = u3/2 V = (u2 - v2 ) = u/2 sin = v/(2V) = 3/2 = 600 angle between v and V = 900 hope this helps!