/*! 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 36 A boat moves through the water o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 36

A boat moves through the water of a river at \(10 \mathrm{~m} / \mathrm{s}\) relative to the water, regardless of the boat's direction. If the water in the river is flowing at \(1.5 \mathrm{~m} / \mathrm{s}\), how long does it Lake the boat to make a round trip consisting of a \(900-\mathrm{m}\) displacement downstream followed by a \(300-\mathrm{m}\) displacement upstream?

Short Answer

Expert verified
The total time for the round trip will be approximately 1.89 minutes.

Step by step solution

01

Identify the Effective Speeds

For the downstream trip, the boat and the river are going in the same direction. So, their speeds will add up. Therefore, effective speed downstream will be \( speed_{boat} + speed_{river} = 10m/s + 1.5m/s = 11.5m/s \). For the upstream trip, the boat is going against the river. So, the river's speed will subtract from the boat's. So, effective speed upstream will be \( speed_{boat} - speed_{river} = 10m/s - 1.5m/s = 8.5m/s \).
02

Compute Time For Each Part of the Journey

To find out the time taken for trip, we use the formula \( Time = Distance / Speed \). So, the time downstream, for the 900m trip will be \( time_{downstream} = 900m / 11.5m/s = 78.26s \) and time upstream, for the 300m trip will be \( time_{upstream} = 300m / 8.5m/s = 35.29s \).
03

Find the Total Time

To find total time for the round trip, we simply add the time taken for the downstream and upstream trips. So, \( time_{total} = time_{downstream} + time_{upstream} = 78.26s + 35.29s = 113.55s \).
04

Convert Seconds to Minutes for Final Answer

Finally, for a more understandable answer, we convert our time from seconds to minutes by dividing by 60. So, the time taken for the round trip in minutes is \( time_{total (minutes)} = time_{total (seconds)} / 60 = 113.55s / 60 = 1.89 minutes \).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relative Velocity
In riverboat problems, understanding relative velocity is crucial. The concept of relative velocity refers to the velocity of an object as observed from a particular frame of reference. In the case of a boat moving across a river, both the boat and the river are in motion.
This means that the boat's velocity relative to the river and the ground are different due to the river's flow.
  • Boat's velocity relative to water: This is simply the speed at which the boat moves through the water.
  • River's velocity: This is the speed of the flow of the river.
  • Boat's velocity relative to ground: To determine this, you must consider both the boat's and the river's speeds.
Understanding these concepts helps in calculating the boat's effective speeds when moving in the same or opposite direction to the river's flow.
Downstream and Upstream Motion
When discussing riverboats, motion can either be downstream or upstream which affects the effective speed.
  • Downstream: In this case, the boat moves in the same direction as the river. Thus, the effective speed is the sum of the boat's speed and the river's speed, as both are working together. This results in a greater speed, making the downstream journey quicker.
  • Upstream: Here, the boat moves against the direction of the current. As a result, the river's speed subtracts from the boat's speed. This decreases the effective speed when compared to downstream, meaning more time is needed for upstream travel.
This understanding forms the basis for solving problems related to downstream and upstream motion in riverboat scenarios, as observed in the exercise.
Time Calculation in Physics
Time calculation is an essential part of riverboat problems and is expressed through the formula for time: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]This simple equation relates the concepts of distance and velocity to find how long a journey will take.
  • For downstream motion, where the boat鈥檚 effective speed increases, the time taken is calculated using the combined speeds of the boat and river.
  • For upstream motion, the journey takes longer because the effective speed is reduced, using the difference between the boat's speed and the river's speed.
  • Finally, for a round trip, simply add the times for both downstream and upstream trips to get the total time.
Having a grasp of these calculations allows one to navigate problems involving moving frames of reference like riverboats effectively.

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

You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity \(\vec{v}\) at an angle \(\theta\) with respect to the horizontal. Let the building be \(50.0 \mathrm{~m}\) tall, the initial horizontal velocity be \(9.00 \mathrm{~m} / \mathrm{s}\), and the initial vertical velocity be \(12.0 \mathrm{~m} / \mathrm{s}\). Choose your coordinates such that the positive \(y\) -axis is upward, the \(x\) -axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.

The determined Wile \(\mathrm{E}\). Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of Acme power roller skates, which provide a constant horizontal acceleration of \(15 \mathrm{~m} / \mathrm{s}^{2}\), as shown in Figure Pg.73. The coyote starts off at rest \(70 \mathrm{~m}\) from the cdge of a cliff at the instant the roadrunner zips by in the direction of the cliff. (a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have to reach the cliff before the coyote. (b) If the cliff is \(100 \mathrm{~m}\) above the base of a canyon, find where the coyote lands in the canyon. (Assume his skates are still in operation when he is in "flight" and that his horizontal component of acceleration remains constant at \(15 \mathrm{~m} / \mathrm{s}^{2} .\) )

A golf ball with an initial speed of \(50.0 \mathrm{~m} / \mathrm{s}\) lands exactly \(240 \mathrm{~m}\) downrange on a level course. (a) Neglecting air friction, what tus projection angles would achieve this result? (b) What is the maximum height reached by the ball, using the two angles determined in part (a)?

An artillery shell is fired with an initial velocity of \(300 \mathrm{~m} / \mathrm{s}\) at \(55.0^{\circ}\) above the horizontal. To clear an avalanche, it explodes on a mountainside \(42.0 \mathrm{~s}\) after firing. What are the \(x\) -and \(y\) -coordinates of the shell where it explodes, relative to its firing point?

The cye of a hurricane passes over Grand Bahama Island in a direction \(60.0^{\circ}\) north of west with a speed of \(41.0 \mathrm{~km} / \mathrm{h}\). Three hours later the course of the hur. ricane suddenly shifts due north, and its speed slows to \(25.0 \mathrm{~km} / \mathrm{h}\). How far from Grand Bahama is the hurricane \(4.50 \mathrm{~h}\) after it passes over the island?
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Physics of Motion

Read Explanation

Force

Read Explanation

Fundamentals of Physics

Read Explanation

Radiation

Read Explanation

Thermodynamics

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.