a 1.5 kg blue ball moves with a speed of 2.5 m/s collides, another 1.5 kg red ball which is at rest. after collision, the blue ball moves off at an angle of 30 deggress to the original direction of motion and the red ball deflects at an angle of theta to the same axis. find the final velocity of each ball and the angle?
Without loss of generality, we may assume that the 1st ball is moving in the +x direction.
After the collision, since the two balls are identical, the resultant v1+v2 will still have the same direction, which means that the two velocities are both 30° from the original v, in opposite directions.
So, one moves at an angle of +30° and the other at an angle of -30°
Now just work out the x- and y-components.
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of Momentum:
The total momentum before the collision is equal to the total momentum after the collision, assuming no external forces act on the system. Mathematically, this can be expressed as:
(mass of blue ball * initial velocity of blue ball) + (mass of red ball * initial velocity of red ball) = (mass of blue ball * final velocity of blue ball) + (mass of red ball * final velocity of red ball)
2. Conservation of Kinetic Energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision. Mathematically, this can be expressed as:
(1/2 * mass of blue ball * (initial velocity of blue ball)^2) + (1/2 * mass of red ball * (initial velocity of red ball)^2) = (1/2 * mass of blue ball * (final velocity of blue ball)^2) + (1/2 * mass of red ball * (final velocity of red ball)^2)
Let's solve these equations step by step:
1. Calculate the initial momentum:
Initial momentum of the blue ball = mass of blue ball * initial velocity of blue ball
= 1.5 kg * 2.5 m/s
= 3.75 kg·m/s
Initial momentum of the red ball (at rest) = mass of red ball * initial velocity of red ball
= 1.5 kg * 0 m/s
= 0 kg·m/s
2. Apply conservation of momentum to calculate the final velocities:
(1.5 kg * 2.5 m/s) + (1.5 kg * 0 m/s) = (1.5 kg * final velocity of blue ball) + (1.5 kg * final velocity of red ball)
3.75 kg·m/s = 1.5 kg · final velocity of blue ball + 1.5 kg · final velocity of red ball
3. Apply conservation of kinetic energy to calculate the angles:
(1/2 * 1.5 kg * (2.5 m/s)^2) + (1/2 * 1.5 kg * (0 m/s)^2) = (1/2 * 1.5 kg * (final velocity of blue ball)^2) + (1/2 * 1.5 kg * (final velocity of red ball)^2)
9.375 J = (0.75 kg * (final velocity of blue ball)^2) + (0.75 kg * (final velocity of red ball)^2)
Solve these two equations simultaneously to find the final velocities and the angles.
Note: Theta is not defined in the question, so we cannot calculate its value unless it is provided.