A hockey player is standing on hisskates when an opposing player skates by with

Question

A hockey player is standing on hisskates when an opposing player skates by with the puck, movingwith a constant speed of 12 m/s. After 3.0 s, the first playermakes up his mind to chase his opponent and starts acceleratinguniformly at 3.8 m/s2. How long does it take him to catch hisopponent? How far does hetravel before he catches up with his opponent? A hockey player is standing on hisskates when an opposing player skates by with the puck, movingwith a constant speed of 12 m/s. After 3.0 s, the first playermakes up his mind to chase his opponent and starts acceleratinguniformly at 3.8 m/s2. How long does it take him to catch hisopponent? How far does hetravel before he catches up with his opponent?

Explanation / Answer

The displacement of the player is    S1 = ut + 0.5 at2       = 0 + 0.5 * 3.8t2 = 1.9t2 At t = 3.0 s , the opponent is So = 36 m from the player. Hisacceleration is zero. ( he is moving with constant speed) The displacement of the opponent is    S2 = So + u t + 0.5at2         = 36 + 12 * t + 0         = 36 + 12 t When the players are side by side then       S1 = S2     1.9 t2 = 36 + 12 t ==> 1.9t2 - 12t - 36 = 0 solving this quadratic equation for time we get       t = 8.53s.

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