Collision of pucks elastic?

[dorian_stokes]

Homework Statement

Consider the collision between two hockey pucks in the figure below. They do not stick together. Their speeds before the collision are v1i = 30 m/s and v2i = 10 m/s. It is found that after the collision one of the pucks is moving along x with a speed of 6 m/s. What is the final velocity of the other puck? v1 is in second quadrant with 30 degrees from x-axis going south east, and v2 is on the y-axis going up.

Homework Equations

30cos30, 30sin30, 10cos270, and 10sin270

The Attempt at a Solution

 

[jbsteele]

v1i = 30cos30 + 30sin30v2i = 10cos270 + 10sin270v1f + v2f = 6 + v2f26.50 + v2f = v2f26.50 = v2fTherefore, the final velocity of the other puck is 26.50 m/s

 

[tomcue]

To determine the final velocity of the other puck, we can use the conservation of momentum and the conservation of kinetic energy equations. Since the pucks do not stick together, the collision is considered to be elastic. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

We can also use the fact that the pucks move along the x and y axes to determine the components of their velocities. We can use the given information to find the initial x and y components of the velocities, which are 30cos30 and 30sin30 for puck 1 and 10cos270 and 10sin270 for puck 2.

Using the conservation of momentum equation, we can set the initial momentum of the system (before the collision) equal to the final momentum of the system (after the collision). This gives us the equation:

(m1*v1i + m2*v2i) = (m1*v1f + m2*v2f)

Where m1 and m2 are the masses of the pucks, v1i and v2i are the initial velocities, and v1f and v2f are the final velocities.

Since we know that puck 1 has a final velocity of 6 m/s along the x-axis, we can substitute this value into the equation and solve for v2f. This gives us the final velocity of puck 2 as 16 m/s along the y-axis, going up.

In conclusion, the final velocity of the other puck is 16 m/s along the y-axis, going up. This collision can be considered elastic since the total kinetic energy before and after the collision is the same. The pucks do not stick together and their velocities are conserved after the collision.