A hockey player is standing on his skates on a frozen pond when anopposing playe

Question

A hockey player is standing on his skates on a frozen pond when anopposing player, moving with a uniform speed of 10 m/s, skates by with the puck.After 4.0 s, the first playermakes up his mind to chase his opponent. If he acceleratesuniformly at 5.0 m/s2, determine each of thefollowing. (a) How long does it take him to catch his opponent? (Assume theplayer with the puck remains in motion at constantspeed.)
(a) How long does it take him to catch his opponent? (Assume theplayer with the puck remains in motion at constantspeed.)

Explanation / Answer

(a) Howlong does it take him to catch his opponent? (Assume the playerwith the puck remains in motion at constant speed.)

position of player but the race starts 4s after so thefirst player distance becomes= 40+10t
position of second player=1/2(a)t^2=1/2*5t^2= 2.5t^2

at what time they have the same displacement

40+10t=2.5t^2
0=2.5t^2 -10t - 40
0=t^2-4t-16
using the quadratic formula
11.403124237432849 and -1.4031242374328485
answer has to be positive so = 11.4 s

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