Flag General Physics> What is the relation between escape veloc...
question mark

What is the relation between escape velocity and projection velocity?

shruti , 9 Years ago
Grade
anser 1 Answers
Riddhish Bhalodia

Last Activity: 9 Years ago

Projection velocity is any velocity with which an object is thrown. While escape velocity is the minimum projection velocity required for object to leave the gravitational field of the planet.
So first lets calculate the vc
We apply energy conservation
1/2mv_c^2 - GMm/R = 0 \quad => \quad v_c = \sqrt{\frac{2GM}{R}}
If the initial velocity = nvc
And the final velocity be v then again applying energy conservation we get
1/2mn^2v_c^2 - GMm/R = 1/2mv^2
2n^2GM/R - 2GM/R = v^2
v = \sqrt{n^2-1}\sqrt{\frac{2GM}{R}} = v_c\sqrt{n^2-1}
Hence option C
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments