Question

A projectile is fired from earth vertically with a
velocity k∅(e) where V(e) is the escape velocity and K is
a constant less than unity. The maximum height to which it rises as measured from the centre of earth
is ? Explain .
​

Answer 1

Answer:

given : V = k Ve ( typo error Phi)

Let

the height above the earth surface be h 

radius of earth be R.

Thus max Dist from the center of earth  r=R+h      

Potential energy of the projectile at maximum height  P.E=mgh/ ( 1+h/R)

Also:  K.E=P.E because Energy remains conserved.

1/2 mV^2= PE

1/2m(KVe)^2=       P.E=mgh/ ( 1+h/R)

Escape velocity = Ve= Root (2gR)

K^2 r = r - R

R = ( 1-K^2)r

r = R/( 1-K^2)