/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 23 A relay race is run along a stra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 23

A relay race is run along a straight-line track of length \(300.0 \mathrm{m}\) running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start line and passes the baton to a third runner who races \(100.0 \mathrm{m}\) northward to the finish line. The magnitudes of the average velocities of the first, second, and third runners during their parts of the race are \(7.30 \mathrm{m} / \mathrm{s}, 7.20 \mathrm{m} / \mathrm{s}\) and \(7.80 \mathrm{m} / \mathrm{s},\) respectively. What is the average velocity of the baton for the entire race? [Hint: You will need to find the time spent by each runner in completing her portion of the race.]

Short Answer

Expert verified
Answer: The average velocity of the baton for the entire race is given by the formula: \(average\_velocity = \frac{100\,\mathrm{m}}{time_1 + time_2 + time_3}\) where time_1, time_2, and time_3 represent the time taken by each runner to complete their part of the race. To find the actual value of the average velocity, substitute the values of time_1, time_2, and time_3 from the solution and solve for the average velocity.

Step by step solution

01

Calculate the time taken by each runner

To find the time taken by each runner to complete their part of the race, we use the formula: time = distance / velocity. For the first runner: \(time_1 = \frac{300.0\,\mathrm{m}}{7.30\,\mathrm{m/s}}\) For the second runner: \(time_2 = \frac{300.0\,\mathrm{m}}{7.20\,\mathrm{m/s}}\) For the third runner: \(time_3 = \frac{100.0\,\mathrm{m}}{7.80\,\mathrm{m/s}}\)
02

Calculate the total time taken by all runners

Now we add up the times calculated in step 1 to find the total time taken by all three runners: \(total\_time = time_1 + time_2 + time_3\)
03

Calculate the total distance traveled by the baton

The first runner travels 300m northward, the second runner travels 300m southward, and the third runner travels 100m northward. Since the directions are opposite for the first two runners, their distances subtract. \(total\_distance = 300\,\mathrm{m} - 300\,\mathrm{m} + 100\,\mathrm{m} = 100\,\mathrm{m}\)
04

Calculate the average velocity of the baton for the entire race

To find the average velocity of the baton for the entire race, we divide the total distance by the total time: \(average\_velocity = \frac{total\_distance}{total\_time}\) Plug the values from steps 2 and 3 into the formula to get the final answer: \(average\_velocity = \frac{100\,\mathrm{m}}{time_1 + time_2 + time_3}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A ball thrown by a pitcher on a women's softball team is timed at 65.0 mph. The distance from the pitching rubber to home plate is \(43.0 \mathrm{ft}\). In major league baseball the corresponding distance is \(60.5 \mathrm{ft}\). If the batter in the softball game and the batter in the baseball game are to have equal times to react to the pitch, with what speed must the baseball be thrown? Assume the ball travels with a constant velocity. [Hint: There is no need to convert units; set up a ratio.]
At 3 P.M. a car is located \(20 \mathrm{km}\) south of its starting point. One hour later it is \(96 \mathrm{km}\) farther south. After two more hours, it is \(12 \mathrm{km}\) south of the original starting point. (a) What is the displacement of the car between 3 P.M. and 6 P.M.? (b) What is the displacement of the car from the starting point to the location at 4 P.M.? (c) What is the displacement of the car between 4 P.M. and 6 P.M.?
You are driving your car along a country road at a speed of $27.0 \mathrm{m} / \mathrm{s} .$ As you come over the crest of a hill, you notice a farm tractor \(25.0 \mathrm{m}\) ahead of you on the road, moving in the same direction as you at a speed of \(10.0 \mathrm{m} / \mathrm{s} .\) You immediately slam on your brakes and slow down with a constant acceleration of magnitude $7.00 \mathrm{m} / \mathrm{s}^{2} .$ Will you hit the tractor before you stop? How far will you travel before you stop or collide with the tractor? If you stop, how far is the tractor in front of you when you finally stop?
For the train of Example \(2.2,\) find the average velocity between 3: 14 P.M. when the train is at \(3 \mathrm{km}\) east of the origin and 3: 28 P.M. when it is \(10 \mathrm{km}\) east of the origin.
To pass a physical fitness test, Massimo must run \(1000 \mathrm{m}\) at an average rate of \(4.0 \mathrm{m} / \mathrm{s} .\) He runs the first $900 \mathrm{m}\( in \)250 \mathrm{s} .$ Is it possible for Massimo to pass the test? If so, how fast must he run the last 100 m to pass the test? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Energy Physics

Read Explanation

Physics of Motion

Read Explanation

Electricity and Magnetism

Read Explanation

Engineering Physics

Read Explanation

Waves Physics

Read Explanation

Oscillations

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.