Question

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 5.0 m/s, skates by with the puck. After 1.50 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.31 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.) (b) How far has he traveled in that time? Step 1 (a) We choose x = 0 to be the initial location of the first player, and t = 0 to be the instant when this player starts to chase his opponent. At this time, the opponent is (1.50 s)·(5.0 m/s) = 7.5 m in front of the first player. We are given that the first player accelerates uniformly at 0.31 m/s2 At time t > 0 the displacements of the first player and his opponent from the origin are xplayer = (x0)player + (v0)player t + 1 2 aplayer t2 = 0 + 0 + 1 2 m/s2 t2 and xopponent = (x0)opponent + (v0)opponent t + 1 2 aopponent t2 = m + m/s t + 0..

Answer 1

Let player 1 be at position ,

Let player 2 is moving at a uniform speed,

At player 1 decides to overtake player 2 and accelerate at

At the position of the player 2 is

Now the player 1 decides to overtake player 2. So let us set the time

Let   be the time taken by the player 1 to catch player 2 ( doesn't include initial ).

The total distance traveled by the player 2 when is,

The total distance traveled by the player 1 can be found out from the equation of motion is

Here is the initial velocity of the player 1 which is zero. a is the acceleration of the player 1 and is the time taken by the player 1 to catch player 2.

Distance traveled by the player 1 at time is,

Since player 1 catches player 2 at time = , the total distance traveled by the player 1 must be equal to the total distance traveled by the player 2. Hence equation (1) is equal to the equation (2).

So (As time cannot have negative value another root of the equation is neglected)

The total distance traveled by player 1(which is same as the distance covered by the player 2). we can use equation (2)