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Problem 65 Hard Difficulty

Find the escape velocity $ v_0 $ that is needed to propel a rocket of mass $ m $ out of the gravitational field of a planet with mass $ M $ and radius $ R $. Use Newton's Law of Gravitation (see Exercise 6.4.33) and the fact that the initial kinetic energy of $ \frac{1}{2} mv^2_0 $ supplies the needed work.


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Related Topics

Integration Techniques

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01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Watch More Solved Questions in Chapter 7

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Problem 82

Video Transcript

the problem is finding escape. We lasted with zero that is needed to propel a rocket of mice Ham a tough the gravitational field off planet of this mask after AM and riders are youth. Newton's law of gravitation and the fact that the initial matic energy off half on with their squire supplies that major work. The first using Newton's slough off gravitation half ofwork made it if they caught you improper, integral from Capt Awar infinity. She have on and over square. Yeah, it should be equal to one half. I'm with Cyril. Squire. We need to find zero the first this improper, Integral. If they caught you, Um um limit a ghost penetrated into grow from capt. Our tow A one over X square. Yes, this is it on lim A cost Vanity one over. Negative one over a wan ho har. This is the captain tree. We are. So we have one half. Um, wait. Zero square. It's the call to G. Over. We can start on you. So we're half read. Zero squire, Shoot house t. Um, For what

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Top Calculus 2 / BC Educators
Catherine Ross

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University of Nottingham

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
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