Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 37

You are on the Moon and would like to send a probe into space so that it does not fall back to the surface of the Moon. What launch speed do you need?

Short Answer

Expert verified
Answer: The minimum launch speed required is 3.122 × 10^5 m/s.

Step by step solution

01

Identify the variables

Identify the variables given in the problem. The mass of the Moon (M_moon) is 7.342 × 10^22 kg, the radius of the Moon (R_moon) is 1.737 × 10^6 m, and the gravitational constant (G) is 6.674 × 10^-11 N m²/kg².
02

Write down the escape velocity formula

Write down the escape velocity formula to find the minimum launch speed: v_escape = sqrt((2*G*M_moon) / R_moon)
03

Insert the given values

Insert the given values into the escape velocity formula: v_escape = sqrt((2*6.674×10^-11 N m²/kg²*7.342×10^22 kg) / 1.737×10^6 m)
04

Perform the calculations

Perform the calculations to find the escape velocity: v_escape = sqrt((2*6.674×10^-11 * 7.342×10^22) / 1.737×10^6) = sqrt(9.738×10^11) = 3.122 × 10^5 m/s
05

Find the required launch speed

The required launch speed to send a probe into space so that it does not fall back to the surface of the Moon is 3.122 × 10^5 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!

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

Use dimensional analysis to show that the electric power output of a wind turbine is proportional to the cube of the wind speed. The relevant quantities on which the power can depend are the length \(L\) of the rotor blades, the density \(\rho\) of air (SI units \(\mathrm{kg} / \mathrm{m}^{3}\) ), and the wind speed \(v\).
A record company executive is on his way to a TV interview and is carrying a promotional CD in his briefcase. The mass of the briefcase and its contents is \(5.00 \mathrm{kg}\) The executive realizes that he is going to be late. Starting from rest, he starts to run, reaching a speed of $2.50 \mathrm{m} / \mathrm{s} .$ What is the work done by the executive on the briefcase during this time? Ignore air resistance.
A car moving at \(30 \mathrm{mi} / \mathrm{h}\) is stopped by jamming on the brakes and locking the wheels. The car skids 50 ft before coming to rest. How far would the car skid if it were initially moving at $60 \mathrm{mi} / \mathrm{h} ?$ [Hint: You will not have to do any unit conversions if you set up the problem as a proportion. \(]\)
Bruce stands on a bank beside a pond, grasps the end of a 20.0 -m-long rope attached to a nearby tree and swings out to drop into the water. If the rope starts at an angle of \(35.0^{\circ}\) with the vertical, what is Bruce's speed at the bottom of the swing?
Human feet and legs store elastic energy when walking or running. They are not nearly as efficient at doing so as kangaroo legs, but the effect is significant nonetheless. If not for the storage of elastic energy, a \(70-\mathrm{kg}\) man running at \(4 \mathrm{m} / \mathrm{s}\) would lose about \(100 \mathrm{J}\) of mechanical energy each time he sets down a foot. Some of this energy is stored as elastic energy in the Achilles tendon and in the arch of the foot; the elastic energy is then converted back into the kinetic and gravitational potential energy of the leg, reducing the expenditure of metabolic energy. If the maximum tension in the Achilles tendon when the foot is set down is \(4.7 \mathrm{kN}\) and the tendon's spring constant is $350 \mathrm{kN} / \mathrm{m},$ calculate how far the tendon stretches and how much elastic energy is stored in it.
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Space Physics

Read Explanation

Energy Physics

Read Explanation

Electricity

Read Explanation

Fundamentals of Physics

Read Explanation

Quantum Physics

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