A ROCKET IS FIRED VERTICALLY FROM THE SURFACE OF MARS WITH A SPEED OF 2km/s IF 20%OF IT'S INITIAL ENERGY IS LOST DUE TO MARTIAN  ATMOSPHERIC RESISTANCE,HOW FAR WILL THE ROCKET GO FROM THE SURFACE OF MARS BEFORE RETURNING TO IT?

 

I HAVE TRIED THIS QUESTION.PLEASE EXPLAIN WHAT'S WRONG IN THIS?

80/100(1/2m*2000*2000+GMm/r)=GMm/(r+h)

where M=mass of mars

r=radius of mars

h=height upto which the rocket would go

Dear swetlina,

When a rocket is fired then as it moves verticaly upwards its kinetic potential energy increases at the expense of its kinetic energy. and it acquires maximum height at a point where its potentil energy is equal to its initial kinetic energy.

However, due atmospheric resistance offered, only 80 percent of its kinetic energy is getting converted into potential energy

so use the formula

(80/100)(1/2m*2000*2000)= maximum potential energy