Question

A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to half the escape velocity for that planet. the maximum height attained by the body is

Answer 1

Answer:

maximum height attained will be 1600 km

Step-by-step explanation:

Given is radius of the planet is r

initial velocity = half of escape velocity

As escape velocity of earth is 11.2 km/s

so initial velocity = 11.2/2

                            =5.6 km/s

It attains the maximum height so final velocity= 0

From second equation of motion we know that

2gh = vf$(final velocity)^{2} - (initail velocity)^2$

here g= gravitaional acceleration which in case = -9.8 m/s²

in form of kilo meter it would be

g= -9.8 *$10^{-3}$ km/s²                     .............(negative sign indicates body is moving upward)

putting the values gives

2 * (-9.8 *$10^{-3}$) * h = 0 - (5.6)²

-19.6 *$10^{-3}$ *h = -31.36

h= $\frac{-31.36}{-19.6 *10^{-3}}$

computing this gives

h=1600 km

Answer 2

Answer: Above picture will definetely help you( H=R/3)

only one point to be noted in picture

here escape velocity is given half of escape velocity