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 47.0 above the horizontal, and aims for a beetle on a leaf 2.60 cm above the water's surface.

a. What is the greatest horizontal distance from which the archerfish can hit the beetle? (in cm)

b. How much time does the beetle have to react in this case? (in seconds)

I CANNOT SEEM TO GET TO THE CORRECT ANSWER NO MATTER WHICH WAY I TRY.

Explanation / Answer

initial speed vo = 2.5 m/s

along horizantal

initial velocity = vox = vo*cos47

horizantal distance = x = vox*T

T = x/vox = x/(2.58cos47)

along vertical

voy = vo*sin47

vertical displacement = y = 2.6 cm = 0.026 m

y = voy*T + 0.5*g*T^2

y = tan47*X - 0.5*g*x^2/(vox)^2

0.026 = tan47*x - 0.5*9.8*x^2/(2.5*cos47)^2

x = 0.611 m = 61.1 cm     <<<<<-------answer

++++

part(b)

T = x/vox

T = 0.611/(2.5*cos47)

T = 0.358 s   <<<<<-------answer

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