Tutorial Exercise A hockey player is standing on his skates on a frozen pond whe

Question

Tutorial Exercise A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 3.0 m/s, skates by with the puck. After 2.10 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.43 m/s2, determine each of the following. (a) How long does it take him to catch his opponent? (Assume the player with the puck remains in motion at constant speed.) (b) How far has he traveled in that time? Step 1 (a) we choose x = 0 to be the initial location of the first player, and t = 0 to be the instant when this player starts to chase his opponent. At this time, the opponent is (2.10 s). (3.0 m/s) = 6.3 m in front of the first player. We are given that the first player accelerates uniformly at 0.43 m/s2 At time t> 0 the displacements of the first player and his opponent from the origin are Xplayer = (xo)player + (vo)player t +-aplayer t2 =0+0+ 0.43 m/s2) t2 and t2 xopponent = (xo)opponent + (vo)opponent t + 2aopponent 3 m/s t 0 mvs)t+ 6.31 m) + 1 3

Explanation / Answer

Xplayer = Xopponent

(0.5) (0.43) t2 = 6.3 + 3t

0.215 t2 - 3 t - 6.3 = 0

t2 + (-3/0.215) t + (-6.3/0.215) = 0

t2 + (- 13.95) t + (- 29.30) = 0

t = 15.8 sec

b)

distance travelled by the first player

Xplayer = (0.5) (0.43) (15.8)2

Xplayer = 53.7 m

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