Question

A rocket is fired from the surface of earth with a speed √2 if 30% energy is lost due

to atmosphere then how far from surface will this rocket reach.​

Answer 1

Answer:

The total initial energy of the rocket and the planet system is the sum of the kinetic energy of the rocket and the gravitational energy of the system.

whereas the final energy will be the gravitational energy at a height H from the surface.

The total energy can be written as:

R

−GMm

​  

+(  

100

80

​  

)  

2

1

​  

mV  

2

=  

R+h

−GMm

​  

+0

Simplify the above expression:

GMm(  

R

1

​  

−  

R+h

1

​  

)=0.4m(2×10  

3

)  

2

 

⇒  

R

GM

​  

(1−  

R+h

R

​  

)=1.6×10  

6

 

=1−  

6.67×10  

−11

×6.4×10  

23

 

3.395×10  

6

×1.6×10  

6

 

​  

 

R+h=  

0.873

R

​  

=3,  

0.873

395

​  

=3,888.9km  

So, the height attained by the rocket from the surface will be

H=3,888.9−3,395=493.9km

Explanation: