Question

if a body is projected vertically upward with velocity and V=nve where and n<1 ve is escape velocity from the surface of Earth then the maximum altitude at height attained by the body is given as​

Answer 1

Answer:

Maximum altitude from surface of Earth is given as

$H = \frac{n^2}{1 - n^2} R$

Explanation:

Here in such type of questions we can use total energy conservation law

So here we will have

$-\frac{GMm}{R} + \frac{1}{2}mv^2 = - \frac{GMm}{r} + 0$

at maximum altitude the speed of the body will become zero

So final kinetic energy must be zero here

$-\frac{GMm}{R} + \frac{1}{2}m(n^2v_e^2) = - \frac{GmM}{r}$

here we have

$v_e = \sqrt{\frac{2GM}{R}}$

so we will have

$-\frac{GMm}{R} + \frac{1}{2}mn^2(\frac{2GM}{R}) = -\frac{GMm}{r}$

$-\frac{1}{R} +\frac{n^2}{R} = -\frac{1}{r}$

$\frac{1}{r} = \frac{1 - n^2}{R}$

$r = \frac{R}{1 - n^2}$

here R = radius of earth

Now maximum altitude of the body is given as

$H = r - R$

$H = \frac{R}{1 - n^2} - R$

$H = \frac{n^2}{1 - n^2} R$

#Learn

Topic : Escape velocity and energy conservation

https://brainly.in/question/5591993