   Chapter 2, Problem 43P

Chapter
Section
Textbook Problem

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 12 m/s, skates by with the puck. After 3.0 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 4.0 m/s2, (a) how long does it take him to catch his opponent, and (b) how far has he traveled in dial time? (Assume the player with the puck remains in motion al constant speed.)

(a)

To determine
The time taken to catch the ball.

Explanation

Given Info: The acceleration of the player is 4.0m/s2 and the velocity of the opponent is 12m/s .

Explanation:

The formula used to calculate the distance covered by the player is,

Δxp=12apt2

Here,

Δxp is the displacement of the player

t is the time taken to catch the ball

ap is the acceleration

Substitute 4.0m/s2 for ap to find Δxp .

Δxp=12(4.0m/s2)t2=(2.0m/s2)t2 (1)

The formula used to calculate the distance covered by the opponent is,

Δxo=vt

Here,

Δxo is the displacement of the opponent

v is the velocity of the opponent

Substitute 12m/s for v to find Δxo .

Δxo=(12m/s)t

The formula used to calculate the distance at which the opponent was opponent is,

Δx'=vt'

Here,

Δx' is the distance at which the opponent is

t' is the time at which the player was not moving

Substitute 12m/s for v and 3.0s for t' to find Δx' .

Δx'=(12m/s)(3

(b)

To determine
The distance travelled by the player.

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