Archerfish are tropical fish that hunt by shooting drops of water from their mou

Question

Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water surface to knock them into the water, where the fish can eat them. A 65-g fish at rest just at the surface of the water can expel a 0.30-g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. The fish shoots the drop of water at an insect that hovers on the water surface, so just before colliding with the insect, the drop is still moving at the speed it had when it left the fishs mouth. In the collision, the drop sticks to the insect, and the speed of the insect and water just after the collision is measured to be 2.0 m/s. What is the insect's mass?

Explanation / Answer

The insect's mass which will be given as :

Using conservation of momentum, we have

mw vw = (mi + mw) vi

rearrange an above above eq.

(mi + mw) = (mw vw / vi)

mi = (mw vw / vi) - mw

where, mw = mass of water = 0.3 g

vw = speed of water = 2.5 m/s

vi = speed of insect = 2 m/s

then, we get

mi = [(0.3 g) (2.5 m/s) / (2 m/s)] - (0.3 g)

mi = (0.375 g) - (0.3 g)

mi = 0.075 g

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