Consider three scenarios for a one-dimensional elastic collision in which a “bullet” is fired at a stationary target. For each scenario, determine the final velocities of both the bullet, v_1f, and the target, v_2f, in terms of the bullet’s initial velocity, v₀. Assume both the bullet and target are on a horizontal surface for which friction is negligible. 

Case (a): Both the bullet and target are bowling balls; m₁ = m₂ = 7.25 kg. 

Case (b): The target is one of the bowling balls, but the bullet is a Styrofoam ball of the same diameter; m₁ = 140 g and m₂ = 7.25 kg. 

Case (c): Now make the Styrofoam ball the target and the bowling ball the bullet; m₂ = 140 g and m₁ = 7.25 kg. Compare parts (b) and (c) to the following extremes: 

(d) when the target is the Earth and the bullet is a tennis ball and 

(e) when the target is a frozen pea and the bullet is a truck’s windshield.