Question

Calculate the velocity of projection of a particle so that the maximum height attained by the particle is .5 R, where R is radius of earth.​

Answer 1

Answer:

As we know that

escape velocity =

2gR

So, V=

2

2gR

=

2

gR

=

2R

GM

Now,

Let the maximum height attained be

′

h

′

then an conserving mechanical energy between point of projection and highest point we get.

(h+R)

+GM

+0=0+

2

1

m(

2R

gM

)

2

h+R

1

=

4R

1

3R=h

h=3R