Question

The radius of Mars (from the center to just above the atmosphere) is (3400 km $\left(3400\times {10}^{3}m\right)$), and its mass is $0.6\times {10}^{24}kg$ . An object is launched straight up from just above the atmosphere of Mars. (a) What initial speed is needed so that when the object is far from Mars its final speed is $1000m/s$? (b) What initial speed is needed so that when the object is far from Mars its final speed is $0m/s$? (This is called the escape speed.)

Short answer

(a) The initial speedwhen the object is far from Marsits final speed is $1000m/s$is $4.827\times {10}^{3}m/s$

(b) The initial speed when the object is far from Mars its final speed is 0 m/s is$4.826\times {10}^{3}m/s$

Step-by-step solution

Identification of given data

• The radius of Mars is 3400 km
• The mass is $0.6\times {10}^{24}kg$
• The final speed is $1000m/s$

Definition of the Escape Speed

The Escape Speed is defined as the minimum speed required to break free an object from the gravitational pull of a planet.

(a) Calculation of the initial speed when the object is far from Mars its final speed is 1000 m/s

The principle of the conservation of energy is the addition of final kinetic and potential energy is equal to the addition of initial kinetic and potential energy,

The expression will be,