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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.

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