Sign up for our free STEM online summer camps starting June 1st!View Summer Courses

University of Delaware

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81

Need more help? Fill out this quick form to get professional live tutoring.

Get live tutoring
Problem 64

Escape Velocity The minimum velocity required for an object to escape Earth's gravitational pull is obtained from the solution of the equation

$\int v d v=-G M \int \frac{1}{y^{2}} d y$

where $v$ is the velocity of the object projected from Earth, $y$ is the distance from the center of Earth, $G$ is the gravitational constant, and $M$ is the mass of Earth. Show that $v$ and $y$ are related by the equation

$v^{2}=v_{0}^{2}+2 G M\left(\frac{1}{y}-\frac{1}{R}\right)$

where $v_{0}$ is the initial velocity of the object and $R$ is the radius of Earth.

Answer

Please see explanation

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

So we're starting with the girl of being. You sleep well to the anti derivatives. Sorry and single. Too negative. Jean Time's intent. Derivatives of one over. Why squared do you want? Well, for the left hand side, This is going to be the squared over to minus the initial. They got squared two. And for the right hand side, you have negative chief times. Save the girl. Why? To the negatives too, Teo, to think all negative G m times negative. Why? To the negative one. My house. Negative. Why not to may of one. And that's equal GM times one over. Why minus one were are because ours the initial there we go hope for homes.

## Recommended Questions