The archerfish hunts by dislodging an unsuspecting insect from its resting place

Question

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 2.45 m/s at an angle of 46.0 above the horizontal, and aims for a beetle on a leaf 4.00 cm above the water's surface.

a. At what horizontal distance (cm) from the beetle should the archerfish fire if it is to hit its target in the least time?
b. How much time will the beetle have to react?

Do not just give me the answer. Please provide detailed explanation.

Explanation / Answer

time taken to reach 4 cm from water surface (will depend on vertical velocity)= 0.04 = 2.45sin(46)*t - 0.5*9.8*t*t t = 0.33 and 0.024 we will take o.33 sec as it longer so the beetle has 0.33s to react horizontal distance = horizontal velocity* time = 2.45*cos(46) * 0.33 = 0.56m

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