A ball with mass m = 0.210 kg and kinetic energy K1 = 2.97 J collides elastically with a second ball of the same mass that is initially at rest. After the collision, the first ball moves away at an angle of = 30.6° with respect to the hori- zontal, as shown in the figure. What is the kinetic energy of the first ball after the collision?

Question

A ball with mass m = 0.210 kg and kinetic energy K1 = 2.97 J collides elastically with a second ball of the same mass that is initially at rest. After the collision, the first ball moves away at an angle of = 30.6° with respect to the hori- zontal, as shown in the figure. What is the kinetic energy of the first ball after the collision?

HELP!
Please step by step

I only got the the first V of M1 that it is 5.31 m/s :/

Answer 1

http://www.sparknotes.com/physics/linearmomentum/collisions/section2.rhtml

Answer 2

To solve this problem step by step, we can use the principles of conservation of momentum and conservation of kinetic energy for an elastic collision.

Step 1: Understand the problem
We are given the mass and initial kinetic energy of the first ball before the collision, as well as the angle at which it moves away after the collision. We need to find the kinetic energy of the first ball after the collision.

Step 2: Calculate the initial velocity of the first ball (v1i)
The given kinetic energy (K1) of the first ball can be expressed as the formula: K1 = (1/2) * m * (v1i)^2, where m is the mass of the ball and v1i is its initial velocity.

Rearranging the formula, we get: v1i = √(2 * K1 / m)

Substituting the given values into the formula, we have: v1i = √(2 * 2.97 J / 0.210 kg)

Evaluating the expression, we find: v1i ≈ 5.31 m/s

Step 3: Conservation of momentum
In an elastic collision, both momentum and kinetic energy are conserved. Since the second ball is initially at rest, the total initial momentum of the system is equal to the momentum of the first ball before the collision.

The initial momentum (p) can be calculated using the formula: p = m * v1i

Substituting the known values, we have: p = 0.210 kg * 5.31 m/s

Evaluating the expression, we find: p ≈ 1.12 kg·m/s

Step 4: Conservation of kinetic energy
Since the collision is elastic, the total kinetic energy after the collision is the same as the total kinetic energy before the collision.

We know that the second ball was initially at rest, so The total kinetic energy before the collision is Ktotal = K1.

Therefore, the kinetic energy of the first ball after the collision (K1f) is equal to Ktotal.

Substituting the known value, we have: K1f = 2.97 J

So, the kinetic energy of the first ball after the collision is 2.97 J.