A Bullet is fired vertically upward it loses 2/3 of its kinetic energy when it rises 75 m, the maximum height bullet can reach is

N=2

Explanation:

We know that at the surface of the earth, value of g=

R

2

GM

At height h above the Earth's surface, the value of acceleration due to gravity g

′

=

(R+h)

2

GM

So it is given that g

′

=

4

g

When the bullet reaches maximum height, acceleration due to gravity is  

4

1

th of that at planet's surface.

That implies  

4R

2

GM

=

(R+h)

2

GM

  →h=R

By conservation of mechanical energy,  

R

−GMm

+

2

1

mv

2

=

h+R

−GMm

+0 since velocity is zero at max height. ⇒

2

1

mv

2

=

2R

GMm

v=

R

GM

=

2R

2GM

=

2

1

R

2GM

=

2

1

v

esc

 ⇒v

esc

=

2

v

⇒N=2