Answer to Question #131923 in Physics for rose auburn

Question

Monkey in a tree. A monkey is hanging from a tree branch. A coconut is fired in a perfectly horizontal direction, toward the monkey as a target. The monkey sees the coconut being fired toward him and lets go of the branch. Assume that the monkey reacts instantaneously. Will the monkey catch the coconut? Suppose that the monkey and the weapon were 25 meters apart and the coconut travels at a speed of 25 m/s. NEGLECTING AIR RESISTANCE, will the monkey catch the coconut??

Answer 1

What we've got here: a monkey falling and increasing speed for 9.8 m/s every single second and a coconut shot horizontally but yet falling as well. As the coconut moves horizontally, it falls vertically with 0 initial vertical speed. To pass 25 meters with 25 m/s will take

$$t=\frac{d}{v}.$$

During this time, the coconut will be lower for the following height:

$$h=\frac{gt^2}{2}=\frac{gd^2}{2v^2}.$$

But how lower will the monkey be when the coconut will pass 25 m horizontally? Right, for the same height:

$$H=\frac{gd^2}{2v^2}.$$

Therefore, no matter how far the coconut is, the monkey will always be able to catch it if the coconut is shot ideally horizontally. The key point here is that we consider both bodies as free falling objects, but one of them meanwhile approaches another.