Question

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 4.0 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 0.14 m/s2, determine each of the following:

a. How long does it take him to catch his opponent?
b. How far has he traveled in that time?

Answer 1

a)
`t=59.817652833125294s \approx 59.8s`

b)
`D_1=894.01m`

Step-by-step explanation:

From the question we are told that

Speed of opposing player
`V_2=4.0m/s`

First player chase his opponent after
`t=2.80t`

Acceleration of first player
`a=0.14 m/s2`

Let time of catch be
`t_c`

a)Generally the Equation for distance covered is mathematically given as follows

Distance to catch First opponent

`D_1=(1)/(2)(0.14)t^2`

`D_1=0.07t^2`

Distance to covered Second opponent

`D_2=(2.8+t)*4`

Generally when first opponent catch the second opponent it is represented mathematically as

`D_2=D_1`

`0.07t^2=(2.8+t)*4`

`0.07t^2=11.2+4t`

`0.07t^2-4t-11.2`

`t=59.817652833125294s \approx 59.8s`

b)Generally the the total time traveled by the first opponent is mathematically given as

`D_1=(t^2)/(4)`

`D_1=(59.8^2)/(4)`

`D_1=894.01m`