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 2.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.44 m/s7, 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?

Answer 1

Given that,

vi(a) = 2 m/s ; t1 = 2.8 s ; a(p) = 0.44 m/s²

(a)Lets suppose that the player is initally at origin, at t= 0 he begins to chase the apponent, At t = 0 the distance of apponent from player is

xi(a) = 2 x 2.8 = 5.6 m

We can write for the displacements of the player for t > 0

x(p) = xi(p) + vi(p) x t + 1/2 x a(p)x t² = 0 + 0 + 1/2 x 0.44 t² =0.22 t²

x(a) = xi(a) + vi(a) x t + 1/2 x a(a) x t² = 5.6 + 2 x t +0 = 5.6 + 2 t

Now when players are side by side, x(p) = x(a)

0.22 t² = 5.6 + 2t

0.22 t² - 2t - 5.6 = 0

This quadratic eqn gives us, t = 11.34 and t = -2.25 but t has to be positive so t = 11.34 sec

Hence, t = 11.34 sec

(b)The distance travelled by player will be simply

x(p) = 0.22 t² = 0.22 x (11.34)² = 28.29 meters

Hence, x(p) = 28.29 meters