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) Five meters per second, (B) 15 meters per second.
Okay, so in this question, we’ve got a diagram showing two arrows. There’s a black arrow and there’s a red arrow. We’re told that these two 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 direction of the arrow gives us the direction of the vector.
In the diagram that we’ve been given, we can see that both of the two arrows are pointing in the same direction to the right. This means that the velocity represented by the red arrow must be in the same direction as the velocity represented by the black arrow. We’re told that the black arrow represents a velocity of 10 meters per second, which is a positive value of velocity. This means that on the horizontal left–right axis, right must be the positive direction. And so all velocities represented by arrows pointing to the right will have positive values. We can see that both of the two possible answers for the velocity represented by the red arrow are positive values, so we can’t rule either of them out on the basis of direction.
The other thing that we can consider is the length of the arrows. Looking at the diagram, it’s clear that the black arrow is longer than the red arrow. Since the length of the arrow tells us the magnitude of the vector, then the longer the arrow, the greater the magnitude of the vector must be. Since the red arrow has a shorter length than the black arrow, then the magnitude of the velocity represented by the red arrow must be smaller than the magnitude of the velocity represented by the black arrow. Since the magnitude of the velocity represented by the black arrow is 10 meters per second, then the red arrow must represent a velocity with a smaller magnitude than 10 meters per second.
Our two available options are five meters per second, which is indeed smaller than 10 meters per second, or 15 meters per second, which is larger than 10 meters per second. So our answer to the question is the value given here in option (A). The red arrow could represent a velocity of five meters per second.
