Question

Determine the velocity required for a moving object 2.00 x 10^4 m above the surface of Mars to escape from Mars's gravity. The mass of Mars is 6.42 x 10^23 kg, and its radius is 3.40 x 10^3 m.

Answer 1

To determine the velocity required for a moving object to escape from Mars's gravity, we can use the escape velocity equation.

Step-by-step explanation:

To determine the velocity required for a moving object to escape from Mars's gravity, we can use the escape velocity equation. The escape velocity, v, is given by the formula:

v = √((2G*M)/(r+h)),

where G is the gravitational constant (6.67 × 10^-11 N·m²/kg²), M is the mass of Mars (6.42 × 10^23 kg), r is the radius of Mars (3.40 × 10^3 m), and h is the height of the object above the surface of Mars (2.00 × 10^4 m).

Substituting the given values into the formula, we can calculate the velocity required for the object to escape from Mars's gravity.

Answer 2

Therefore the escape velocity from Mar's gravity is
`15.88 * 10^4` m/s.

Step-by-step explanation:

Escape velocity: Escape velocity is a the minimum velocity that a object needs to escape from the gravitational field of massive body.

`V_(escape)=\sqrt{(2GM)/(R)}`

`V_(escape)=` Escape velocity

G=Universal gravitational constant = 6.673×10⁻¹¹N m²/Kg²

M= mass of Mars = 6.42×10²³ kg

R = Radius of the Mars = 3.40×10³m

The escape velocity does not depend on the velocity of a object.

`V_(escape)=\sqrt{(2*6.673* 10^(-11)* 6.42* 10^(23))/(3.40*10^3)}`

`=15.88 * 10^4` m/s

Therefore the escape velocity from Mar's gravity is
`15.88 * 10^4` m/s.