Home
Class 11
PHYSICS
A rocket is fired vertically from the su...

A rocket is fired vertically from the surface of Mars with a speed of `2kms^(-1)`. If `20%` of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of Mars before returning to it? Mass of Mars `=6.4xx10^(23)kg`, radius of Mars `=3395 km`,

Text Solution

Verified by Experts

The correct Answer is:
1655
Total energy of the rocket
`E=(1)/(2)mv^(2)-(GMm)/(R)`
Since 20% energy is lost, hence energy remained
`=80%orE=(80)/(100)E=(4)/(5)E=(4)/(5)[(1)/(2)mv^(2)-(GMm)/(R)]`
At the highest point, distant h from the surface of mars, its total energy will be potential, Hence
`(4)/(5)[(1)/(2)mv^(2)-(GMm)/(R)]=-(GMm)/(R+h)`
or `(2)/(5)m(v^(2)-(2GM)/(R))=-(GMm)/(R+h)`
or `(2)/(5)(v^(2)R-2GM)/(R)=-(GM)/(R+h)`
or `R+h=-(5RGM)/(2(v^(2)R-2GM))`
But `R=3395km=3395xx10^(3)m`,
`G=6.67xx10^(-11)Nm^(2)kg^(-2)`
`M=6.4xx10^(23)kg,v=2kms^(-1)=2xx10^(3)ms^(-1)`
`therefore R+h`
`=-(5xx3395xx10^(3)xx6.67xx10^(-11)xx6.4xx10^(23))/(2[(2xx10^(3))^(2)xx3395xx10^(3)-2xx6.67xx10^(-11)xx6.4xx10^(23)])`
`=-(7.25xx10^(20))/(2[1.36xx10^(13)-8.54xx10^(13)])`
`=(7.25xx10^(7))/(2xx7.18)=5.05xx10^(6)m`
or`h=5.05xx10^(6)-3395xx10^(3)`
`=1655xx10^(3)m=1655km`
Promotional Banner

Similar Questions

Explore conceptually related problems

A rocket is fired fired vertically from the surface of Mars with a speed of 2 Kms^(-1) . If 20% of its initial energy is lost due to martain atmospheric resistance, how far will the rocket go from the surface of Mars before returning to it ? Mass of Mars= 6.4xx10^(23) Kg, radius of Mars=3395 Km, G= 6.67xx10^(-11)Nm^(2)Kg^(-2) .

A rocket is fired vertically from the surface of mars with a speed of 2 km/s. If 20% of its initial energy is lost due to martian atmosphere resistance how far (in km) will the rocket go from the surface of mars before returning to it? Mass of mars =6.4xx10^(23) kg, radius of mars =3395 km, G=6.67xx10^(-11)Nm^(2)//kg^(2) .

A rocket of mass m is field vertically from the surface of Mars of mass M , radius R with a sped upsilon . If 20% of its initial energy is lost due to Martain atmosheric resistance, how far will the rocket go from the surface of Mars before returing to it? Let G be the gravational constant.

A rocket is launched vertical from the surface of the earth of radius R with an initial speed v . If atmospheric resistance is neglected, then maximum height attained by the rocket is

A rocket is launched vertically from the surface of earth with an initial velocity v . How far above the surface of earth it will go? Neglect the air resistance.

Calculate the escape speed of a body from the surface of a planet of mass 6.4 xx 10^(23) kg and radius 3400 km.

A projectile is fired vertically from the earth's surface with an initial speed of 10 km//s . Neglecting air drag, how high above the surface of earth will it go?

A rocket is fired vertically with a speed of 5 kms^(-1) from the earth's surface. How far from the earth does the rocket go before returning to the earth ? Mass of earth= 6.0xx10^(24) kg, mean radius of the earth = 6.4xx10^(6) m, G= 6.67xx10^(-11)Nm^(2)Kg^(-2).

A rocket fired from the earth's surface ejects 1% of its mass at a speed of 2000 ms^(-1) in the first second. Find the average acceleration of the rocket in the first second.