A park ranger wants to shoot a monkey hanging from a branch of a tree with a tranquilizing dart. The ranger aims directly at the monkey, not realizing that the dart will follow a parabolic path and thus will fall below the monkey. The monkey, however, sees the dart leave the gun and lets go of the branch to avoid being hit. Will the monkey be hit anyway? Does the velocity of the dart affect your answer, assuming that it is great enough to travel the horizontal distance to the tree before hitting the ground? Defend your answer.
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In this scenario, when the park ranger shoots the dart, it will follow a parabolic path due to the force of gravity acting on it. The monkey, being aware of the dart, decides to let go of the branch in order to avoid getting hit.
Now, let's consider the factors that could determine whether or not the dart will still hit the monkey. First, the velocity of the dart should be taken into account. If the velocity is high enough, the dart will travel a longer horizontal distance before hitting the ground.
However, regardless of the velocity, the monkey will not be hit by the dart. This is because as soon as the monkey lets go of the branch, it starts falling under the influence of gravity. As a result, the monkey will fall vertically downwards while the dart continues its parabolic path. Since the monkey is falling directly downwards while the dart follows a curved path, their paths will not intersect.
In conclusion, the dart will miss the monkey because the monkey falls downwards while the dart follows a parabolic path. The velocity of the dart does not affect this outcome.
Based on the given information, the monkey will not be hit by the dart. The reason for this is the principle of projectile motion.
When the ranger shoots the dart, it follows a parabolic path due to the force of gravity acting on it. The path of the projectile is determined by its initial velocity and launch angle. Since the ranger aims directly at the monkey, the initial velocity of the dart will have two components: horizontal and vertical.
The horizontal component of the dart's velocity remains constant throughout its flight. This means that the dart will travel a certain horizontal distance before hitting the ground, assuming its initial velocity is great enough.
On the other hand, the vertical component of the dart's velocity is affected by the force of gravity, causing it to decrease over time. This means that the dart will start to fall below the horizontal line as it travels toward the monkey.
When the monkey sees the dart leaving the gun and lets go of the branch, it starts to fall as well. However, since the dart is already falling below the monkey's starting position, it will not be hit by the dart.
The velocity of the dart does not affect this outcome. The only factor that affects the outcome is the initial angle of the dart's trajectory. In this case, the monkey successfully avoids being hit.