- #1

- 10

- 1

- Homework Statement
- The radius of Mars (from the center of just above the atmosphere) is 3400 km, and its mass is 6 × 1023 kg. An object is launched straight up from just above the atmosphere of Mars. What initial speed (vi) is needed so that when the object is far from Mars, its final speed (vf) is 500 m/s?

- Relevant Equations
- G = 6.7E-11

Conservation of energy principle: U1 + K1 = U2 + K2

U1 = -GMm/r

K1 = (1/2)mvi^2

U2 = as r approaches infinity, U2 approaches zero

K2 = (1/2)mvf^2

(1/2)mvi^2 - GMm/r = (1/2)mvf^2 + 0

vi = √(vf^2 + (2GMm)/r) = √(250,000 + 2(6.7 E-11)(6 E23)/3400) = 153776.815

But that is not the correct answer, can anybody see my mistake/misunderstanding?

K1 = (1/2)mvi^2

U2 = as r approaches infinity, U2 approaches zero

K2 = (1/2)mvf^2

(1/2)mvi^2 - GMm/r = (1/2)mvf^2 + 0

vi = √(vf^2 + (2GMm)/r) = √(250,000 + 2(6.7 E-11)(6 E23)/3400) = 153776.815

But that is not the correct answer, can anybody see my mistake/misunderstanding?