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 2.00 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.24 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.)

Answer 1

Answer:

18.47 s

Explanation:

Given:

Speed of the opponent, u₁ = 2 m/s

Time after which player starts = 2 seconds

Thus,

distance covered (s₁) by the opponent before the player starts = u₁ × 2

= 2 × 2 = 4 m

let 't' seconds be the time taken by the player to catch the opponent

now,

the total distance covered by the player will be

= 4 m + distance traveled by the opponent in the time t

= 4 + ( 2 × t ) m

also,

From Newton's equation of motion  the distance covered by the player

$s_2=ut+\frac{1}{2}at^2$

where,  

s is the distance

u is the initial speed  = 0 m/s as starting from rest

a is the acceleration  = 0.24 m/s²

t is the time

on substituting the respective values, we get

$s_2=0\times t+\frac{1}{2}\times0.24\times t^2$

also,

s₁ = s₂

thus,

$4 + 2\times t=0\times t+\frac{1}{2}\times0.24\times t^2$

or

4 + 2t = 0.12t²

or

0.12t² - 2t - 4 = 0

on solving the quadratic equation, we get

t = 18.47 s

[negative value of the roots is ignored as time cannot be negative]