A hockey player is standing on his skates on a frozen pond when an opposing play
ID: 1625819 • Letter: A
Question
A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 2.0 m/s, skates by with the puck. After 1.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.38 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.)
s
(b) How far has he traveled in that time?
m
Explanation / Answer
(a) First we need to determine the distance traveled by his opponent.
The initial condition when the hockey player decide to give chase, the distance between them is
x = v*ti = 2 m/s * 1.80 s = 3.6 m
During the chase,
The distance traveled by his opponent is:
x = v*t
The distance traveled by the chasing hockey player is
x + 3.6 m = 0.5*a*t^2
Combine the two equations we get:
v*t + 3.6 m = 0.5at^2
0.5at^2 - vt - 3.6 = 0
Plug in known equations and solve for t:
0.5*0.38*t^2 - 2*t - 3.6 = 0
0.19t^2 - 2t - 3.6 = 0
Using the quadratic formula:
t = 12.07 sec, t = -1.55
Time cannot be negative, so the answer is:
t = 12.07 sec
(b) Since the hockey player starts from rest (v0 = 0), the distance traveled is
x = 0.5at^2 = 0.5*0.38*(12.07)^2 = 27.68 m
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