Chapter 1: Q107PP (page 271)

Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s 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 speed of the archerfish immediately after it expels the drop of water? (a) 0.0025 m/s; (b) 0.012 m/s; (c) 0.75 m/s; (d) 2.5 m/s.

Short Answer

Expert verified

The correct answer is (b) $0.012 m / s$ .

Step by step solution

Identification of given data

The velocity of water is $v_{w} = 2.5 m / s$ .

The mass of water is $m_{w} = 0.3 \times 10^{- 3} k g$ .

The mass of fish is $m_{f i s h} = 65 \times 10^{- 3} k g$ .

The velocity of insect is $v_{i} = 2 m / s$ .

The time is $t = 5 \times 10^{- 3} s$ .

The momentum of the fish is the same for the drop of water is $p_{w a t e r} = 7.5 \times 10^{- 4} k g \cdot m / s$

Concept/Significance of change in Conservation of Momentum

The final total momentum is zero, so apply the law of conservation of momentum

$m_{1} v_{1} - m_{2} v_{2} = 0 m_{1} v_{1} = m_{2} v_{2}$

The expression to calculate the required velocity is given by,

$p_{water} = m_{fish} v_{fish} . . . . . . (1)$

Determine the speed of the archerfish immediately after it expels the drop of water

Substitute $m_{f i s h} = 65 \times 10^{- 3} k g$ , and $p_{w a t e r} = 7.5 \times 10^{- 4} k g \cdot m / s$ in the equation (1) to find the speed of the archerfish.

$7.5 \times 10^{- 4} k g . m / s = v_{f i s h} (65 \times 10^{- 3} k g) v_{f i s h} = \frac{7.5 \times 10^{- 4} k g . m / s}{65 \times 10^{- 3} k g} = 0.012 m / s$

Therefore, the correct answer is (b) 0.012 m/s.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Identification of given data

Concept/Significance of change in Conservation of Momentum

Determine the speed of the archerfish immediately after it expels the drop of water

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

Nuclear Physics

Linear Momentum

Modern Physics

Thermodynamics

Force

Study anywhere. Anytime. Across all devices.