How do you find the kinetic energy lost in this problem?

Question

A 76g particle moving with an initial speed of 150 m/s in the positive x direction strikes and sticks to an 80g particle moving with 72 m/s in the positive y direction.
How much kinetic energy is lost in this collision? Answer in units of J.

Answer 1

Start by using conservation of momentum to find the final velocity of the two particles stuck together. The formula is p_0 = p_f ==> (mv)_0 = (mv)_f, where p is momentum, m is mass, v is velocity, _0 indicates initial conditions, and _f indicates final conditions. Remember that momentum in the x- and y-directions are independent of each other, and momentua of independent bodies in a system are additive. Once you know the x- and y-components of the final velocity, use the Pythagorean theorem to find the magnitude of the final velocity. Finally, calculate the initial kinetic energy (KE = 0.5*mv^2) of the two particles (separately, and then add the values) and the final kinetic energy of the two-particle system (as a single mass with one velocity), and take their difference.