Nomenclature is like this
u1xi = initial speed of moving ball in x-direction
u2xi = initial speed of stationary ball in x-direction
u1yi = initial speed of moving ball in y-direction
u2yi = initial speed of stationary ball in y-direction
V1 = final speed of initially moving ball
V2 = final speed of initially stationary ball
In a perfectly elastic collision
Suppose final velocity of stationary billiard ball is v2 and
it's making angle with horizontal
axis
Using momentum conservation in x direction,
Pi = Pf
m1*u1xi + m2*u2xi = m1*V1x + m2*V2x
given that m1 = m & m2 = m
u1xi = 3 m/sec & u2xi = 0 (since stationary)
V1x = V1*cos 30 deg & V2 = V2*cos
m*u1xi + m*u2xi = m*V1*cos(30 deg) + m*V2*cos
u1xi + u2xi = V1*cos(30 deg) + V2*cos
3 - 0 = V1*cos(30 deg) + V2*cos
V1*cos(30 deg) + V2*cos = 3
V2*cos = 3 - V1*cos 30 deg
Using momentum conservation in y direction,
Pi = Pf
m1*u1yi + m2*u2yi = m1*V1y + m2*V2y
given that m1 = m & m2 = m
u1yi = 0 m/sec & u2yi = 0 m/sec
V1y = V1*sin 30 deg & V2y = -V2*sin
m*u1i + m*u2i = m*V1*sin(30 deg) - m*V2*sin
u1i + u2i = V1*sin(30 deg) - V2*sin
0 - 0 = V1*sin(30 deg) - V2*sin
V1*sin(30 deg) = V2*sin
V2*sin = (1/2)*V1
Now square and add both equation
V2^2*(sin2 + cos2) = (1/4)*V1^2 + 9 + (3/4)*V1^2 - (3*sqrt 3)*V1
V2^2*(1) = (1/4)*V1^2 + 9 + (3/4)*V1^2 - (3*sqrt 3)*V1
V2^2 = (1/4)*V1^2 + 9 + (3/4)*V1^2 - (3*sqrt 3)*V1
V2^2 = V1^2 + 9 - (3*sqrt 3)*V1
Now Using energy conservation in elastic collision
KEi = KEf
0.5*m*u1^2 + 0.5*m*u2^2 = 0.5*m*V1^2 +0.5*m*V2^2
u1^2 + u2^2 = V1^2 + V2^2
V1^2 + V2^2 = 3^2 + 0
V1^2 + V2^2 = 9
V2^2 = 9 - V1^2
Using above expression
9 - V1^2 = V1^2 + 9 - (3*sqrt 3)*V1
2*V1^2 - (3*sqrt 3)*V1 = 0
V1 = (3*sqrt 3)/2
V1 = 2.598 m/sec = 2.6 m/sec
So,
V2 = sqrt (9 - V1^2)
V2 = sqrt (9 - 2.598^2)
V2 = 1.50 m/sec = final speed of stationary billiard ball
Please Upvote.
Comment below if you have any doubt.
1. A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball...
A billiard ball moves at a speed of 4.00m/s and collides elastically with an identical stationary ball. As a result, the stationary ball flies away at a speed of 1.69m/s, as shown in Figure A2.12. Determine the final speed and direction of the incoming ball after the collision. the direction of the stationary ball after the collision. A billiard ball moves at a speed of 4.00 m/s and collides elastically with an identical stationary ball. As a result, the stationary...
Part C: Linear Momentum Problem Cl: (Elastic Collision) A billiard ball moving at 3m/s collides elastically with an identical ball at rest. The final speed of the first ball is 2m/s. At what angles to the original direction do the balls move off? that
A cue ball moving at 2.8 m/s collides elastically with a stationary 8 ball of identical mass. The 8 ball then moves away at an angle of 28 degrees from the direction of the incoming cue ball. What is the speed of the cue ball after the elastic collision?
1- Billiard ball A with mass 0.81 kg collides head on and elastically with billiard ball B (same mass) at rest. Knowing that Ball A moved at 3.41 m/s before collision, what is the speed of Ball B after the collision? 2- A 4.78 kg cube sits on a frictionless surface. A 11.99 gram bullet traveling at 388.07 m/s is shot into the brick and they move together at a certain speed. What is the speed in m/s? 3- What is...
One 1.4kg billiard ball traveling at 3.2 m/s collides with a stationary billiard ball. If the stationary billiard ball bounces at 30 degrees above the original direction, what speed did the first ball bounce at if it went 60 degrees below the original direction.
A billiards ball moving at speed v collides elastically with an identical, stationary ball. Kinetic energy is conserved in the collision. After the collision, the first ball heads off at an angle theta relative to its original direction and at a speed v/2 . What is the speed of the second ball?
A stationary billiard ball with a mass of 0.17kg, is sturck by an identical ball moving at 4.0 m/s. After the collision, the second ball moves 60 degrees to the left of its original direction. The stationary ball movies 30 degrees to the right of the moving ball's original direction. What is the velocity of each ball after the collision? A stationary billiard ball, with a mass of 0.17 kg, is struck by an identical ball moving at 4.0 m/s....
A billiard ball moving at a speed of 7.95 m/s strikes an identical stationary ball a glancing blow. After the collision, one ball is found to be moving at a speed of 1.80 m/s in a direction making a 59.5 ° with the original line of motion. What is the speed of the other ball? At what angle is it moving? Give your answer in degrees. (Hint: use conservation of linear momentum)
Collisions and Kinetic Energy ** Two billiard balls are initially traveling toward each other with Ball 1 having a velocity of 2.00 m/s to the right and Ball 2 having a velocity of 8.00 m/s to the left. The balls undergo an elastic, head-on collision. Find their final velocities. (Define the positive direction to be to the right.) Part 1 + First consider two identical objects with equal mass, one is at rest and the other has a velocity of...
10. A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30 Degree to the original path, determine a. the speed of the first ball after the collision. b. the speed and direction of the second ball after the collision.