Initial speed of an object launched from Mars

Thread starter marjine
Start date Mar 16, 2023
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Initial initial speed Mars Speed

AI Thread Summary

The discussion focuses on calculating the initial speed of an object launched from Mars using gravitational potential energy and kinetic energy equations. The user initially miscalculated the initial velocity due to incorrect unit conversion of the radius from kilometers to meters. After correcting the radius, the calculation yielded a revised initial speed of approximately 153,776.815 m/s. The importance of unit consistency in physics calculations is emphasized. The user expresses gratitude for the assistance in identifying the mistake.

Mar 16, 2023

marjine

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?

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Mar 16, 2023

nasu

Homework Helper

The radius (r) is given in km, isn't it?

Mar 16, 2023

marjine

nasu said:

The radius (r) is given in km, isn't it?

omg... converted it to m and fixed it, thank you so much

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