Question

A zookeeper finds an escaped monkey sitting on top of a light pole. Aiming her tranquilizer gun at the monkey, the zookeeper kneels 10.0 m from the light pole, which is 5.00 m high. The tip of her gun is 1.00 m above the ground and the gun makes an angle with the horizontal of 21.8°. The monkey tries to trick the zookeeper by dropping a banana, then continues to hold onto the light pole. At the moment the monkey releases the banana, the zookeeper shoots. If the tranquilizer dart travels at 50.0 m/s, will the dart hit the monkey, the banana, or neither one?

Answer 1

The answer relies on the calculations of projectile motion to understand if the tranquilizer dart will hit the monkey, the banana, or neither. This takes into account the given vertical and horizontal distances, the angle, and the velocity of the dart, along with the effects of gravity on the falling objects.

Step-by-step explanation:

To determine if the tranquilizer dart will hit the monkey, the banana, or neither one, we must consider the principles of projectile motion. Given the height of the light pole (5.00 m), the height of the tip of the gun (1.00 m), and the distance from the zookeeper to the pole (10.0 m), along with the angle of elevation (21.8°) and the velocity of the dart (50.0 m/s), we can calculate the trajectory of the dart.

We know that the banana and the monkey will fall with the same acceleration due to gravity, so they will be at the same vertical position throughout their fall. By calculating the time it takes for the dart to reach the vertical height where the monkey and banana would be at the time of firing, and then comparing this to the horizontal position, we can determine whether the dart will hit its target.