A monkey is hanging from a branch in a tree. The monkey looks hungry and you want to throw a coconut to him. However, the monkey is nervous and, as soon as he sees something being thrown at him, he lets go of the branch. (The monkey apparently knows that in previous versions of this problem, a hunter was trying to shoot it, so the monkey is understandably a bit nervous.) Knowing the monkey will let go as soon as the coconut is thrown, where should you aim? a) Above the monkey b) At the monkey c) Below the monkey.
What You Need
- "monkey"—(represented by a pie pan or lid of a metal container). See Figure 11-1.
- "coconut"—(represented by a projectile from Project 8)
- DC power supply
- insulated wire—about 25 feet
- switch that opens the circuit at the precise moment the projectile is launched. This can be accomplished by assembling two pieces of metal foil in front of the launcher. At the instant the projectile emerges, it pushes the foil apart, opening the circuit. See Figure 11-2 for a simple way to set this up. There are also optical techniques to do this, some of which are commercially available.
- laser pointer
- various types of the monkey and coconut apparatus are also available commercially
- Set up the apparatus, as shown in Figure 11-3.
- Apply the DC voltage to the electromagnet circuit.
- Arm the launcher (by pushing the ball in with the plunger in the case of the PASCO launcher).
- Close the switch.
- Aim the launcher directly at the target, either visually or aided by the laser pointer.
- Shoot the projectile. As the projectile emerges from the launcher, it causes the switch to open and deactivates the electromagnet. This releases the metal lid (monkey) as the projectile is shot at it.
The answer to the question posed previously is: b) firing at the monkey. As long as the monkey is in range, firing directly at the monkey will cause a direct hit every time.
Why It Works
Both the monkey and the coconut are subjected to the same gravitational acceleration. If the coconut is aimed directly at the monkey in the tree, the coconut will fall from that straight line path and follow the curved (parabolic) path that projectiles normally take. See Figure 11-4. As a result, the coconut falls away from that straight-line path at precisely the same rate as the monkey falls downward. This causes the monkey and the coconut to be in the same place before the monkey hits the ground.
Other Things to Try
Suppose our monkey gets tired of having coconuts thrown at him. Where should he aim a coconut of his own that he throws to deflect the one that is thrown at him? This can be set up using two projectile launchers, but it requires much more precision because the balls have a small diameter. The answer is the same as the previous one. The monkey should aim directly at the hunter.
This project illustrates one of the underlying concepts of projectiles, which is the idea that the horizontal and vertical components of motion are completely independent and do not influence each other. The monkey does not have horizontal motion, but the coconut does. They both have vertical motion, which experiences the same rate of acceleration, regardless of the horizontal motion.