Video Transcript
The arrows shown represent velocities. The black arrow represents a velocity of 10 meters per second. Which of the following velocities could the red arrow represent? (A) Negative five meters per second. (B) Negative 15 meters per second.
Okay, so in this question, we’ve got a diagram showing both a black arrow and a red arrow. The question tells us that these arrows represent velocities. And we can recall that velocity is a vector quantity, which means that it has both a magnitude and a direction. Whenever a vector quantity is represented by an arrow like the ones in this diagram, then the length of the arrow tells us about the magnitude of the vector and the arrow’s direction gives us the direction of the vector.
In the diagram we’re being shown, we can see that the black arrow is pointing to the right. We are told that this arrow represents a velocity of 10 meters per second. This velocity of 10 meters per second is a positive value. This means that along the horizontal left–right axis, right must be the positive direction. So, all velocities represented by arrows pointing to the right must have positive values. And if this is the case, then all velocities represented by arrows pointing to the left must be negative. Since the red arrow in the diagram is pointing to the left, then it must represent a negative value of velocity. Our two available choices are negative five meters per second and negative 15 meters per second. Since both of these velocities are negative, then we can’t rule out either answer on the basis of direction.
The other thing to consider is the length of the arrows. In the diagram, we can see that the black arrow extends from its tail at this horizontal position to its tip at this position. Meanwhile, the red arrow extends from its tail at this horizontal position to its tip all the way over here. The red arrow is clearly longer than the black arrow. And since the length of the arrow tells us the magnitude of the vector, then this longer red arrow must represent a velocity with a greater magnitude than the black arrow. Since the black arrow represents a velocity with a magnitude of 10 meters per second, then the magnitude of the velocity represented by the red arrow must be greater than 10 meters per second.
Option (A) is a velocity of negative five meters per second, and the magnitude of this is five meters per second. This is smaller than a magnitude of 10 meters per second. And so, negative five meters per second can’t be our answer. Option (B) is a velocity of negative 15 meters per second. The magnitude of this, 15 meters per second, is greater than 10 meters per second. So, the velocity of negative 15 meters per second agrees with our requirements for the velocity represented by the red arrow. This means that our answer to the question is that the velocity that the red arrow could represent is negative 15 meters per second, which is the answer given here in option (B).