Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 79

During an ice-skating extravaganza, Robin Hood on Ice, a 50.0 -kg archer is standing still on ice skates. Assume that the friction between the ice skates and the ice is negligible. The archer shoots a \(0.100-\mathrm{kg}\) arrow horizontally at a speed of \(95.0 \mathrm{~m} / \mathrm{s} .\) At what speed does the archer recoil?

Short Answer

Expert verified
Answer: The archer recoils at a speed of approximately 0.19 m/s in the opposite direction to the arrow's motion.

Step by step solution

01

Identify the knowns and the unknowns

In this exercise, the known quantities are: - The mass of the archer, \(m_1 = 50.0\,\text{kg}\) - The mass of the arrow, \(m_2 = 0.100\,\text{kg}\) - The speed of the arrow after being shot, \(v_2 = 95.0\,\text{m/s}\) We need to find the recoil speed of the archer, which we will denote as \(v_1\).
02

Apply the law of conservation of momentum

The total momentum of the system (archer + arrow) must remain constant before and after the arrow is shot. Initially, the momentum is zero, as both the archer and the arrow are stationary. After shooting, we can apply the equation: $$m_1 v_1 + m_2 v_2 = 0$$ We are trying to find the value of \(v_1\), the speed at which the archer recoils.
03

Solve the equation for the unknown

We can rearrange the equation from step 2 to isolate \(v_1\): $$v_1 = -\frac{m_2 v_2}{m_1}$$ Now, we can plug in the known values and calculate the recoil speed of the archer: $$v_1 = -\frac{(0.100\,\text{kg})(95.0\,\text{m/s})}{(50.0\,\text{kg})}$$
04

Calculate the recoil speed

After plugging in the known values, we can find the magnitude of the recoil speed: $$v_1 \approx -0.19\,\text{m/s}$$ We can observe that the value of \(v_1\) is negative which implies that the archer's recoil is in the opposite direction compared to the arrow's motion. Thus, the archer recoils at a speed of approximately \(0.19\,\text{m/s}\) in the opposite direction to the arrow's motion.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The electron-volt, \(\mathrm{eV},\) is a unit of energy \((1 \mathrm{eV}=\) \(\left.1.602 \cdot 10^{-19} \mathrm{~J}, 1 \mathrm{MeV}=1.602 \cdot 10^{-13} \mathrm{~J}\right) .\) Since the unit of \(\mathrm{mo}\) mentum is an energy unit divided by a velocity unit, nuclear physicists usually specify momenta of nuclei in units of \(\mathrm{MeV} / c,\) where \(c\) is the speed of light \(\left(c=2.998 \cdot 10^{9} \mathrm{~m} / \mathrm{s}\right) .\) In the same units, the mass of a proton \(\left(1.673 \cdot 10^{-27} \mathrm{~kg}\right)\) is given as \(938.3 \mathrm{MeV} / \mathrm{c}^{2} .\) If a proton moves with a speed of \(17,400 \mathrm{~km} / \mathrm{s}\) what is its momentum in units of \(\mathrm{MeV} / \mathrm{c}\) ?

Which of the following statements about car collisions are true and which are false? a) The essential safety benefit of crumple zones (parts of the front of a car designed to receive maximum deformation during a head-on collision) results from absorbing kinetic energy, converting it into deformation, and lengthening the effective collision time, thus reducing the average force experienced by the driver. b) If car 1 has mass \(m\) and speed \(v\), and car 2 has mass \(0.5 m\) and speed \(1.5 v\), then both cars have the same momentum. c) If two identical cars with identical speeds collide head on, the magnitude of the impulse received by each car and each driver is the same as if one car at the same speed had collided head on with a concrete wall. d) Car 1 has mass \(m,\) and car 2 has mass \(2 m .\) In a head-on collision of these cars while moving at identical speeds in opposite directions, car 1 experiences a bigger acceleration than car 2 . e) Car 1 has mass \(m\), and car 2 has mass \(2 m\). In a headon collision of these cars while moving at identical speeds in opposite directions, car 1 receives an impulse of bigger magnitude than that received by car 2.

In a severe storm, \(1.00 \mathrm{~cm}\) of rain falls on a flat horizontal roof in \(30.0 \mathrm{~min}\). If the area of the roof is \(100 \mathrm{~m}^{2}\) and the terminal velocity of the rain is \(5.00 \mathrm{~m} / \mathrm{s}\), what is the average force exerted on the roof by the rain during the storm?

A bungee jumper with mass \(55.0 \mathrm{~kg}\) reaches a speed of \(13.3 \mathrm{~m} / \mathrm{s}\) moving straight down when the elastic cord tied to her feet starts pulling her back up. After \(0.0250 \mathrm{~s},\) the jumper is heading back up at a speed of \(10.5 \mathrm{~m} / \mathrm{s}\). What is the average force that the bungee cord exerts on the jumper? What is the average number of \(g\) 's that the jumper experiences during this direction change?

A rocket works by expelling gas (fuel) from its nozzles at a high velocity. However, if we take the system to be the rocket and fuel, explain qualitatively why a stationary rocket is able to move.
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Thermodynamics

Read Explanation

Waves Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Fluids

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free