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Chapter 1: Q106PP (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 momentum of one drop of water immediately after it leaves the fish鈥檚 mouth? (a) 7.5脳10-4鈥�kg鈰�m/s; (b) role="math" localid="1667981772098" 1.5脳10-4kg鈰�m/s; (c) 7.5脳10-3kg鈰�m/s; (d) 1.5脳10-3kg鈰�m/s.

Short Answer

Expert verified

The correct answer is (a) 7.5脳10-4kg鈰�m/s.

Step by step solution

01

Identification of given data

The velocity of water is vw=2.5m/s.

The mass of water is mw=0.3脳10-3kg.

The mass of fish is mfish=65脳10-3kg.

The velocity of insect is vi=2鈥�m/s.

The time is .t=5脳10-3鈥�s

The momentum of the fish is the same for the drop of water ispwater=7.5脳10-4kg鈰�m/s

02

Concept/Significance of Momentum

The momentum of any object can be obtained by multiplying the mass of that object with speed of that object.

The expression to calculate the momentum of the droplet is given by,

pd=mwvw鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�......(1)

03

Determine the momentum of one drop of water immediately after it leaves the fish’s mouth

Substitute mw=0.3脳10-3kg, andvw=2.5鈥�m/s in the equation (1) to find the momentum of one drop of water.

role="math" localid="1667986703621" pd=0.3脳10-3kg2.5m/s=7.5脳10-4kg.m/s

Therefore, the correct answer is (a) 7.5脳10-4kg.m/s.

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