/*! 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 63 A hunter wishes to cross a river... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 63

A hunter wishes to cross a river that is \(1.5 \mathrm{~km}\) wide and flows with a speed of \(5.0 \mathrm{~km} / \mathrm{h}\) parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of \(12 \mathrm{~km} / \mathrm{h}\) with respect to the water. What is the minimum time necessary for crossing?

Short Answer

Expert verified
The minimum time needed for the hunter to cross the river is the result obtained after calculation in minutes. This value, to an appropriate number of significant figures, is the short answer.

Step by step solution

01

Compute for Speed Against the Current

The speed of the boat with respect to the water is given as \(12 \mathrm{~km/h}\). However, the boat has to resist the current of the river in order to get across. This means that the effective speed of the boat across the river can be obtained by drawing or considering a right-angled triangle whereby, the hypotenuse is the boat's maximum speed (\(12 \mathrm{~km/h}\)) and one side of the triangle is the speed of the current (\(5 \mathrm{~km/h}\)). Using Pythagoras theorem, the effective speed, \(V_{\text{eff}}\) of the boat across the river (the other side of the triangle) can be given as \(\sqrt{{12^2 - 5^2}}\). Calculate \(V_{\text{eff}}\).
02

Calculate the Minimum Time Necessary for Crossing the River

The time, \(T_{\text{min}}\), it takes to cross the river can be obtained by using the formula \(T_{\text{min}} = \frac{D}{V_{\text{eff}}}\), where \(D\) is the distance across the river. Substitute the given values and calculate \(T_{\text{min}}\).
03

Convert the Time to Appropriate Units

In general, time is often expressed in minutes or seconds for ease of understanding. Hence, the time \(T_{\text{min}}\) obtained from step 2 should be converted from hours to minutes by multiplying by 60.

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

The magnitude of vector \(\overrightarrow{\mathbf{A}}\) is \(35.0\) units and points in the direction \(325^{\circ}\) counterclockwise from the positive \(x\)-axis. Calculate the \(x\)-and \(y\)-components of this vector.

One of the fastest recorded pitches in major-league baseball, thrown by Tim Lincecum in 2009 , was clocked at \(101.0 \mathrm{mi} / \mathrm{h}\) (Fig. P3.22). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, \(60.5 \mathrm{ft}\) away?

\(\mathrm{M}\) A car travels due east with a speed of \(50.0 \mathrm{~km} / \mathrm{h}\). Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of \(60.0^{\circ}\) with the vertical. Find the velocity of the rain with respect to (a) the car and (b) the Earth.

S In a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the counter and strikes the floor at distance \(d\) from the base of the counter. If the height of the counter is \(h\), (a) find an expression for the time \(t\) it takes the cup to fall to the floor in terms of the variables \(h\) and \(g\). (b) With what speed does the mug leave the counter? Answer in terms of the variables \(d, g\), and \(h .\) (c) In the same terms, what is the speed of the cup immediately before it hits the floor? (d) In terms of \(h\) and \(d\), what is the direction of the cup's velocity immediately before it hits the floor?

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of \(24.0^{\circ}\) below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of \(4.00 \mathrm{~m} / \mathrm{s}^{2}\) for a distance of \(50.0 \mathrm{~m}\) to the edge of the cliff, which is \(30.0 \mathrm{~m}\) above the ocean. Find (a) the car's position relative to the base of the cliff when the car lands in the ocean and (b) the length of time the car is in the air.
See all solutions

Recommended explanations on Physics Textbooks

Electrostatics

Read Explanation

Radiation

Read Explanation

Solid State Physics

Read Explanation

Translational Dynamics

Read Explanation

Energy Physics

Read Explanation

Further Mechanics and Thermal Physics

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.