A hockey puck is sliding due East on a frictionless ice surface. A player strikes it, applying an average force directed exactly North-West. If the puck's speed immediately after the strike is identical to its speed before the strike, what is its new direction of motion?

Step-by-step solution

Let the initial velocity be v _i = v i (due East). The average force, and therefore the change in velocity v , is directed North-West. Thus, v = k(- i + j ) for some positive constant k . The final velocity is given by v _f = v _i + v . v _f = v i - k i + k j = (v - k) i + k j . We are given that the final speed equals the initial speed, so | v _f| = v . (v - k)^2 + k^2 = v^2 v^2 - 2vk + 2k^2 = v^2 2k^2 - 2vk = 0 Since k > 0 , we have k = v . Substituting k = v back into the expression for final velocity: v _f = (v