Answer to Question #292372 in Physics for Ally

Question

A hockey puck B rests in a smooth ice surface and is struck by a second puck A,

which was originally traveling at 40.0 m/s and is deflected 30.0° from its original

direction. The pucks have the same mass. (a) Compute the speed of each puck after

the collision. (b) What fraction of the original kinetic energy of puck A dissipates

during collision?

Answer 1

Conservation of momentum by axes:

$$0=mu_A\sin\theta_A+mu_B\sin\theta_B,\\ mv_A=mu_A\cos\theta_A+mu_B\cos\theta_B.\\\space\\ 0=u_A\sin\theta_A+u_B\sin\theta_B,\\ v_A=u_A\cos\theta_A+u_B\cos\theta_B.\\\space\\ u_A =29.3 \text{ m/s},\\ u_B =20.1 \text{ m/s}.$$

The fraction of energy:

$$ϵ_E =\dfrac{v_A^2 −u_A^2}{v_A^2} =0.46.$$