particle is projected from the surface of the planet Krypton with a speed equal to 3.6 times the escape speed from that planet's surface. When the particle is very far away from Krypton, its speed is N times the escape speed from that planet's surface. What is N?

N = 3.46

Explanation:

The escape velocity on a planet is given by the expression

V_e = √2GM / R

G, M and R are gravitational constant, mass and radius of the planet respectively.

Potential energy at the surface

- GMm / R

Total energy at the surface

= - GMm / R + 1/2 m x (3.6V_e) ²

- GMm / R + 1/2 m x 12.96 x2GM / R

= 11.96 GMm / R

Total energy at infinity

1 / 2 m v² + 0 (potential energy is zero at infinity)

1/2 mv²

Applying conservation of energy

1/2 m v² = 11.96 GMm / R

v = √11.96 √2GMm / R

v = √11.96 x escape velocity at planet.

= 3.46 times

N = 3.46