An eagle swoops down to catch a baby rabbit. The rabbit sees the eagle and starts to run. An all-out chase ensues with the rabbit running east at 4.4 meters per second and the eagle pursuing at 5.6 meters per second.
A. What is the relative velocity of the predator to prey?
B. Will the eagle catch the rabbit?
C. Why or why not will the eagle catch the rabbit?
The correct answer and explanation is:
A. Relative Velocity of the Predator to Prey
The relative velocity of the predator (eagle) to the prey (rabbit) is the difference in their velocities. Since both are moving in the same direction (east), we subtract the rabbit’s speed from the eagle’s speed.
Relative velocity = Velocity of the eagle – Velocity of the rabbit
Relative velocity = 5.6 m/s – 4.4 m/s
Relative velocity = 1.2 m/s
So, the relative velocity of the eagle to the rabbit is 1.2 meters per second.
B. Will the Eagle Catch the Rabbit?
Yes, the eagle will catch the rabbit. The reason for this is that the relative velocity between the eagle and the rabbit is positive, meaning the eagle is moving faster than the rabbit.
C. Why or Why Not Will the Eagle Catch the Rabbit?
The eagle will catch the rabbit because the relative velocity is positive and the eagle is faster. This means that for every second, the eagle gets 1.2 meters closer to the rabbit. Over time, this difference accumulates, and the eagle will eventually close the gap. The chase may take some time depending on how far apart the two are when it starts, but because the eagle is faster, it will ultimately catch up.
In this scenario, the speed advantage of the eagle ensures that it will close the distance between them. The rabbit, although running at a decent speed, is slower than the eagle and cannot escape once the chase begins, as the eagle’s relative speed toward the rabbit is nonzero. Therefore, with enough time, the eagle will inevitably catch the rabbit.