The small archerfish (length 20 to 25 cm) lives in brackish waters of Southeast

Question

The small archerfish (length 20 to 25 cm) lives in brackish waters of Southeast Asia from India to the Philippines. This aptly named creature captures its prey by shooting a stream of water drops at an insect, either flying or at rest. The bug falls into the water and the fish gobbles it up. The archerfish has high accuracy at distances of 1.2 m to 1.5 m, and it sometimes makes hits at distances up to 3.5 m. A groove in the roof of its mouth, along with a curled tongue, forms a tube that enables the fish to impart high velocity to the water in its mouth when it suddenly closes its gill flaps. Suppose the archerfish shoots at a target that is 2.35 m away, measured along a line at an angle of 30.0° above the horizontal. With what velocity must the water stream be launched if it is not to drop more than 2.60 cm vertically on its path to the target?

Explanation / Answer

along horizantal

vox = vo*cos30

x = 2.35 m

ax = 0

x = vox*t

t = x/vox.......(1)

along vertrcial

initial velocity = voy = vo*sin30

acceleration ay = -9.8 m./s^2

y = voy*t + 0.5*ay*t^2 ....(2)

1 & 2

y = tan30*x - 0.5*g*x^2/(vo^2*(cos30)^2))

x =2.35

y = 0.026 m

0.026 = tan30*2.35 - 0.5*g*2.35^2/(vo^2*(cos30)^2))

vo = 5.2 m/s <<<<-------answer

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