A hockey player is standing on his skates on a frozen pond when an opposing play

Question

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 4.0 m/s, skates by with the puck. After 2.20 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.26 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.) 17.34 You may have assumed the players meet when they have equal speed rather than the same location.s (b) How far has he traveled in that time? 39.07 You appear to have calculated your answer to this part of the problem correctly from your answer to the first part, but because your first answer was incorrect this answer is also incorrect. m

Explanation / Answer

a] Let x be the distance covered by the opponent.

x = vt + 4(2.2) = 4t + 8.8

the distance covered by the first player is:

x = ut + (1/2)at2 = 0 + (1/2)(0.26)t2

4t + 8.8 = 0.13t2

solve the quadratic for t to get:

t = 32.831 s

this is the time in which the opponent is caught.

b] In this time, the opponent has traveled a distance:

x = 4(32.831) + 8.8 = 140.124 m.

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