Question

Determine the velocity with which a body must be thrown vertically upwards from the surface of esrth so that it reaches a height of 10r

Answer 1

The gravitational potential on Earth's surface

=U(R)=− GMm/R

Now at a distance 10 R from the Earth's surface its 11 R from the centre. Thus gravitational potential  

= U(11R)= − GMm/11R

Change in PE

=U(11R)−U(R)  

=− GMm/11R−(−− GMm/R) =− 10GMm/11R

This difference is = to the initial kinetic energy=  1/2mv2 (v=initial velocity)

Now, =1/2mv2=10gmM/11r

V = √((20GMm)/11R)

 

Now substituting the respective values, we get:

V = √(((20×(6.7×〖10〗^(-11) )(6×〖10〗^24 ))/(11×(6.4×〖10〗^6 ) )))  

= 1.07×〖10〗^4m/s