Kinematics Forces: Help with Archerfish Targeting & Reaction Time

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The discussion focuses on calculating the optimal horizontal distance for an archerfish to target a beetle using projectile motion principles. The fish expels water at a speed of 1.6 m/s at a 59.0° angle, aiming to hit a beetle located 3.0 cm above the water's surface. To determine the firing distance, the speed must be broken into x and y components, and the time for the water to reach the beetle can be calculated using the vertical height equation. The time available for the beetle to react is also derived from these calculations. The thread emphasizes the importance of using kinematic equations to solve the problem effectively.
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Can anyone Help with this ?

As discussed in Example 4-7, the archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish's mouth. Suppose the archerfish squirts water with a speed of 1.6 m/s at an angle of 59.0° above the horizontal, and aims for a beetle on a leaf 3.0 cm above the water's surface.

-At what horizontal distance from the beetle should the archerfish fire if it is to hit its target in the least time?

-How much time will the beetle have to react?

Thanks
 
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Break up the speed into x and y components. You have an equation which solves for y height. You can use that one to solve for the time. Then, you should know how to do the rest ;)
 

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