Final answer:
The monkey must compensate for the zookeeper's horizontal movement by dropping the coconut before he directly passes underneath. By calculating the time it takes the coconut to fall 20 m, the distance the zookeeper covers can be accounted for, allowing the coconut to land on the zookeeper's toes.
Step-by-step explanation:
To determine how the coconut should be dropped by the monkey to hit the zookeeper's toes, we need to consider the timing and motion of both the falling coconut and the moving zookeeper. The coconut is in free fall, so the only force acting on it is gravity. The zookeeper moves horizontally with a constant speed of 1.5 m/s.
If the monkey drops the coconut directly overhead, it will not hit the zookeeper's toes because the zookeeper is moving forward. To compensate for this, the monkey needs to drop the coconut before the zookeeper reaches the point directly beneath the tree. The exact timing can be calculated by finding the time it takes for the coconut to fall 20 m to the ground using the formula t = √(2h/g), where h is the height and g is the acceleration due to gravity (approximately 9.8 m/s²). Once the time is calculated, the monkey can then drop the coconut earlier by the distance the zookeeper travels in that time, which is speed multiplied by the time.
For a quick estimation, assuming it takes roughly 2 seconds for the coconut to fall (since t = √(2*20/9.8) ≈ 2), the monkey would need to drop the coconut when the zookeeper is about 3 meters (1.5 m/s * 2 s) away from the point directly below.