Calculating the Minimum Velocity of a Pygmy Blowgun Dart

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To calculate the minimum velocity of a pygmy blowgun dart needed to pierce a monkey, one must consider both kinetic energy (KE) and potential energy (PE) due to the dart's vertical ascent. The dart must achieve a speed of at least 4 m/s upon impact, requiring an analysis of the dart's trajectory at an angle of 85 degrees and a vertical height of 35 meters. The relationship between KE and PE indicates that as the dart rises, its kinetic energy decreases while potential energy increases, necessitating a higher initial velocity to compensate for the height. The calculations involve determining the initial velocity needed to ensure that the dart maintains at least 4 m/s upon reaching the monkey. Understanding these dynamics is crucial for solving the problem effectively.
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Pygmies use blow-guns and 15 gram (0.015 kg) darts dipped in the poison curare to immobilize and kill monkeys that live in the tree-top canopy of their forest home. Assume a pygmy at ground level blows a dark at 85 degrees (relative to the horizontal) at a monkey that is 35 vertical meters up. Assuming a dart must be moving at 4m/s to effectively pierce a monkey skin, what is the minimum velocity the dart must be moving as it leaves the blow-gun if it is to pierce the monkey?

now I know that Ill have to use delta KE to find the minimum velocity but I am not quite sure what to do with the vertical height and the degrees
 
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I moved this post to a new thread ; don't hijack threads of other posters for your own homework problems ; start a new thread.

Also, provide some work on it before we help...
 
In problems like this, what can you say about the relationship between KE and PE?
 

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