The Monkey and the Coconut
Overview
"The Monkey and the Coconut" is a classic thought experiment used to illustrate the effect of the gravitational force on a projectile.
A coconut tree is growing in the middle of a small river. Two monkeys arrive at the bank and notice a small ripe coconut about to fall into the river. In order to get the coconut, the monkeys make a plan: On the count of three, the first monkey will shake the tree, while the other will jump across the river and catch the coconut as it falls, landing on the far bank.
How should the second monkey aim her jump in order to catch the coconut?
Adjust the monkey's initial speed and jump angle so that she catches the coconut.
Jump angle =
Speed=
Note: Air resistance is negligible, and time has been slowed down.
Explanation
Why does the monkey always catch the coconut if she aims directly for it (and fast enough)?
Remember:
There are two components of a projectile: horizontal and vertical.
The influence of gravity only acts on the vertical component.
The horizontal component of the projectile does not experience any acceleration.
Equations of the distance traveled by the monkey and the coconut:
Coconutx = 0
Monkeyx = v⋅cosθ
Coconuty = h − 12 gt2
Monkeyy = v⋅ sinθ ⋅t − 12 gt2
h − 12 gt2
=
v⋅ sinθ ⋅t − 12 gt2
h
v⋅ sinθ ⋅ t
t
hv⋅sinθ
The term 12gt2 are on both sides, and can be cancelled out.
As long as initial velocity is high enough the monkey will catch the coconut if she aims directly for it.
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