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 1.20 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.18 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?

Answer needs to be in correct sig figs

Answer 1

You have not mentioned how many significant figures is needed.

Answer 2

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a) Time to Catch Opponent ($t$)

1. Distance covered by Player 2 during the delay:

   $$d_{\text{delay}}=v_2\times t_{\text{delay}}=4.0\text{m/s}\times 1.20\text{s}=4.8\text{m}$$

3. Equation for Player 1's position (accelerating from rest):

   $$d_1=\frac{1}{2}{a}_1{t}^2=\frac{1}{2}(0.18)t^2=0.09t^2$$

5. Equation for Player 2's position (constant speed):

   $$d_2=d_{\text{delay}}+v_{2}t=4.8+4.0t$$

7. Set $d_1=d_2$ to find catch time ($t$):

   $$0.09t^2=4.8+4.0t$$

   Rearrange into standard quadratic form:

   $$0.09t^2-4.0t-4.8=0$$

8. Solve the quadratic equation:
   Using the quadratic formula $t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$:

9. 
   

   Answer: 45.6 s (rounded to 3 significant figures).

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b) Distance Traveled by Player 1

Using $t=45.6\text{s}$ in Player 1's position equation:

$$d_1=0.09t^2=0.09(45.6{)}^2=0.09\times 2079.36\approx 187\text{m}$$

Answer: 187 m (rounded to 3 significant figures).