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Chapter 2: Problem 43

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of \(12 \mathrm{~m} / \mathrm{s}\), skates by with the puck. After \(3.0 \mathrm{~s}\), the first player makes up his mind to chase his opponent. If he accelerates uniformly at \(4.0 \mathrm{~m} / \mathrm{s}^{2}\), (a) how long does it take him to catch his opponent, and (b) how far has he traveled in that time? (Assume the player with the puck remains in motion at constant speed.)

Short Answer

Expert verified
The time it takes the hockey player to catch his opponent is found out in Step 2 and the distance he traveled to catch his opponent is found out in Step 3. Insert the figures from Step 1 in the formulas in Step 2 and 3 for the respective solutions.

Step by step solution

01

Calculate the Relative Speed of Two Players

The first player starts to chase the opponent after 3.0 seconds. By this time, the opponent has traveled a distance. Calculate this distance using the formula \(distance = speed * time\). Here, speed = 12 m/s and time = 3 seconds. This will give the head start distance of the opponent player.
02

Calculate the Time Required to Cover This Distance

Now the player starts to chase his opponent. The player is accelerating at 4.0 m/s^2. Their initial speed was zero. Therefore, use the equation of motion \(time = \sqrt{(2*distance)/acceleration}\) to find out how long it takes for the player to cover the distance that the opponent player has travelled as the head start.
03

Calculate the Total Distance Covered

Now, to find out how far the first player had to travel to catch up with the opponent, use the formula \(distance = (1/2) * acceleration * time^2\). Here, acceleration is 4 m/s^2 and time is the time calculated in Step 2. This will give us the total distance covered by the first player.

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Most popular questions from this chapter

Two cars travel in the same direction along a straight highway, one at a constant speed of \(55 \mathrm{mi} / \mathrm{h}\) and the other at \(70 \mathrm{mi} / \mathrm{h}\). (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination \(10 \mathrm{mi}\) away? (b) How far must the faster car travel before it has a 15 -min lead on the slower car?

A student throws a set of keys vertically upward to his fraternity brother, who is in a window a distance \(h\) above. The brother's outstretched hand catches the keys on their way up a time \(t\) later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (Answers should be in terms of \(h, g\), and \(t\).)

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A truck tractor pulls two trailers, one behind the other, at a constant speed of \(100 \mathrm{~km} / \mathrm{h}\). It takes \(0.600 \mathrm{~s}\) for the big rig to completely pass onto a bridge \(400 \mathrm{~m}\) long. For what duration of time is all or part of the trucktrailer combination on the bridge?

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