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CaptainTrips
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Billiard Balls--Elastic Collision
I'm going through my old homework problems to prepare for the AP exam, and I got this right back in December, but now I have no idea how to solve it
A cue ball traveling at 7.0 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. Find:
a) the angle between the velocity vectors of the two balls after the collision
b) the speed of each ball after the collision
KE = 1/2mv2
p = mv
The collision is elastic, so both kinetic energy and momentum are conserved, so
1/2mv02 = 1/2mv12 + 1/2 mv22
v02 = v12 + v22
and
mv0 = mv1 + mv2
v0 = v1 + v2
The x component of the cue ball's final velocity is v1cos30
The x component of the target ball's final velocity is v2cosΘ
this gives me two equations, and three unknowns:
49 = (v1cos30)2 + (v2cosΘ)2
7 = v1cos30 + v2cosΘ
Am I missing something that will tell me the angle of the velocity of the second ball? Thanks
I'm going through my old homework problems to prepare for the AP exam, and I got this right back in December, but now I have no idea how to solve it
Homework Statement
A cue ball traveling at 7.0 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. Find:
a) the angle between the velocity vectors of the two balls after the collision
b) the speed of each ball after the collision
Homework Equations
KE = 1/2mv2
p = mv
The Attempt at a Solution
The collision is elastic, so both kinetic energy and momentum are conserved, so
1/2mv02 = 1/2mv12 + 1/2 mv22
v02 = v12 + v22
and
mv0 = mv1 + mv2
v0 = v1 + v2
The x component of the cue ball's final velocity is v1cos30
The x component of the target ball's final velocity is v2cosΘ
this gives me two equations, and three unknowns:
49 = (v1cos30)2 + (v2cosΘ)2
7 = v1cos30 + v2cosΘ
Am I missing something that will tell me the angle of the velocity of the second ball? Thanks