Question

The escape speed of a projectile on the Earth's surface is 11.2 km s⁻¹. A body is projected out with thrice this speed. What is the speed of the body far away from the Earth? Ignore the presence of the Sun and other planets.

Answer 1

Hii dear,

◆ Answer- 31.68 km/s

◆ Explaination-
# Given-
ve = 11.2 km/s
vp = 3×ve

# Formula-
Let, v' be the belocity of the projectile far away from the earth.

Total energy of the projectile on the Earth,
E1 = (1/2)mvp^2 – (1/2)mve^2

Total energy of the projectile far away from the Earth
E2 = (1/2)mv'^2

By law of conservation of energy, we have
E1 = E2
(1/2)mvp^2 – (1/2)mve^2 = (1/2)mv'^2
v' = √(vp^2 – ve^2)
v' = √[(3ve)^2 – ve^2]
v' = √8 × ve
v' = 2.83 × 11.2
v' = 31.68 km/s

Velocity of projectile far from earth will be 31.68 km/s

Hope that is useful...