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 2.50 m/s at an angle of 55.0 above the horizontal, and aims for a beetle on a leaf 4.00 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? ......I got t=.0205 ms and x=.029 cm but it was wrong?

Explanation / Answer

Least possible time

So in the projectile motion, the nearest distance should be answer

given h = 4cm

So 0.04 = 2.5 * sin (55) t - 0.5 *9.8 * t^2

So t = 0.0205 seconds = 20.5 milliseconds ( check units)

x = 2.5 * cos(55 ) * 0.0205

= 0.029m = 2.9 cm ( check units)

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