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Chapter 1: Q108PP (page 271)

Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water鈥檚 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.

What is the average force the fish exerts on the drop of water? (a) 0.00015 N; (b) 0.00075 N; (c) 0.075 N; (d) 0.15 N.

Short Answer

Expert verified

The correct answer is (d) 0.15 N.

Step by step solution

01

Identification of given data

The velocity of water is vw=2.5鈥�m/s.

The mass of water is mw=0.3脳10-3kg.

The velocity of insect is vi=2鈥�m/s.

The time is t=5脳10-3鈥�s.

02

Concept/Significance of change in Momentum and average force

The initial speed of the water is zero, so the change in momentum for the water is,

螖辫=mwvw鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�......(1)

The average force is given by,

Favg=螖辫t鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�......(2)

03

Determine the average force the fish exerts on the drop of water

Substitute vw=2.5鈥�m/s, andmw=0.3脳10-3kg in the equation (1) to find the change in momentum.

鈭�p=0.3脳10-3kg2.5m/s=7.5脳10-4kg.m/s

Substitute 螖p=7.5脳10-4kg鈰�m/s, andt=5脳10-3鈥�s in the equation (2) to find the average force.

Favg=7.5脳10-4kg.m/s5脳10-3s=0.15N

Therefore, the correct answer is (d) 0.15 N.

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