Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 12

Can the resultant of two velocities have zero magnitude? If so, give an example.

Short Answer

Expert verified
If possible, provide an example. Answer: Yes, the resultant of two velocities can have zero magnitude if the two velocities are equal in magnitude but opposite in direction. For example, if one velocity is 5 m/s East and the other is 5 m/s West, their resultant will be 0 m/s.

Step by step solution

01

Understanding Velocity as a Vector Quantity

Velocity is a vector quantity, meaning it has both magnitude and direction. When dealing with vectors, we can use graphical or mathematical methods to add them. In this problem, we are interested in determining if adding two velocities can result in a vector with zero magnitude.
02

Adding Two Vectors

To determine if two velocities can have a resultant with zero magnitude, we need to remember how to add vectors. The principle of vector addition states that if you place the tail of one vector at the head of another, the resultant vector extends from the tail of the first vector to the head of the second vector. In mathematical terms: Resultant Vector (R) = Vector A + Vector B, where A and B are the two velocities.
03

Condition for Zero Magnitude

For the resultant of two vectors to have zero magnitude, the two vectors need to be equal in magnitude but opposite in direction. Mathematically, this can be expressed as: Vector A + Vector B = 0, or Vector A = -Vector B
04

Example of Two Velocities with Zero Magnitude Resultant

Based on the condition in Step 3, let's provide an example. Suppose Vector A represents a velocity of 5 m/s to the right (east), and Vector B represents a velocity of 5 m/s to the left (west). In this case: Vector A = 5 m/s East Vector B = 5 m/s West (-5 m/s East) Adding the two velocities, we get: Resultant Vector (R) = Vector A + Vector B = 5 m/s East + (-5 m/s East) = 0 m/s In this situation, the two velocities have a resultant with zero magnitude, so it is indeed possible for the resultant of two velocities to have zero magnitude.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

What are the "basic" or "fundamental" physical quantities? Why are they called that?

Explain what a “derived unit” of measure is.

A pendulum clock is taken to a repair shop. Its pendulum is replaced by a shorter one that oscillates with a smaller period than the original. What effect, if any, does this have on how the clock runs?

Using concepts and physical quantities discussed in this chapter, explain why it is usually safe for a person standing on the seat of a chair to jump horizontally and land on the floor, but not for a person standing on the roof of a tall building to jump horizontally and land on the ground.

A ball thrown at a brick wall bounces directly back with the same speed it had when it struck the wall. Has the velocity of the ball changed? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Measurements

Read Explanation

Thermodynamics

Read Explanation

Classical Mechanics

Read Explanation

Oscillations

Read Explanation

Rotational Dynamics

Read Explanation

Medical 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.

Sign-up for free