# Horizontal Velocity in Monkey-Dart Problem

In summary, the Monkey-Dart experiment involves a monkey letting go of a vine at the same time a dart is shot at him. The dart is known to reach the monkey because the distance from the vine to where he ends up is equal to the difference between where the dart was aimed and where the dart ends up, which is both 1/2gt^2. The horizontal velocity of the dart increases as the angle alpha decreases, but the angle is fixed and it is the initial speed of the dart that may vary. Within this range of speed, the dart will always hit the monkey, regardless of the angle. The lower curves have a lower horizontal velocity, but this does not affect the outcome of the experiment.
In the Monkey-Dart experiment (where a monkey let's go of a vine exactly the same time a dart is shot at him), the dart is known to reach the monkey because the distance from the vine to where he ends up is equal to difference between where the dart was aimed and where the dart ends up : both 1/2gt^2.

My question is that the horizontal velocity of the dart obviously increases as Alpha (the angle the dart was shot upwards at) decreases. Meaning if the dart is shot directly up (90 degrees), the dart has no horizontal velocity. So if the lower curves have a higher horizontal velocity (vcos(alpha)) as we know they do, how is it that it takes them longer to get to the SAME x position than it takes one of the trajectories with a higher alpha angle?

Thanks!

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You are not interpreting the problem correctly. The angle alpha is fixed as determined by the monkey's height and distance from the initial start point of the dart. It is the initial speed of the dart that may be varied, from an arbitrarily high value of unimaginable speed, to a relatively low value sufficient to reach the monkey before it hits the ground. Within this range of speed, with the dart fired at the angle alpha, the dart will always hit the monkey (ignoring air resistance of course). The lower curves have a lower horizontal velocity.

That is a well formulated and logical answer. I sincerely thank you for making understand.

## 1. What is horizontal velocity in the monkey-dart problem?

Horizontal velocity in the monkey-dart problem refers to the speed at which the dart travels horizontally towards the monkey. It is a crucial factor in determining whether the dart will hit the monkey or not.

## 2. How is horizontal velocity calculated in the monkey-dart problem?

Horizontal velocity can be calculated using the formula v = d/t, where v is the horizontal velocity, d is the horizontal distance traveled, and t is the time taken. This formula assumes that there is no acceleration present.

## 3. Why is horizontal velocity important in the monkey-dart problem?

Horizontal velocity is important because it determines whether the dart will reach the monkey or not. If the horizontal velocity is too low, the dart may fall short and miss the monkey. If it is too high, the dart may overshoot the monkey.

## 4. How does horizontal velocity affect the outcome of the monkey-dart problem?

The horizontal velocity directly affects the horizontal distance traveled by the dart. If the horizontal velocity is too low, the dart may not reach the monkey. If it is too high, the dart may hit the monkey with too much force, causing harm.

## 5. Can horizontal velocity be changed in the monkey-dart problem?

Yes, horizontal velocity can be changed by adjusting the angle at which the dart is thrown or by changing the initial speed of the dart. However, changing the horizontal velocity may also affect the vertical velocity and the trajectory of the dart.

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