Solve for Escape Velocity on Mars: Differential Equation Method

AI Thread Summary
The discussion focuses on calculating the escape velocity from Mars using a differential equation approach. The acceleration due to gravity on Mars is given as 0.38g, and its radius is 2100 miles. Participants express confusion regarding the formulation of the differential equation, noting the limited variables provided. The key equation for solving the problem is v^(2) = [2gR^(2) / r] + C, which relates velocity to gravitational forces and distance. Clarification on how to derive the differential equation is sought to further understand the escape velocity calculation.
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Homework Statement


The acceleration of gravity on the surface of Mars is 0.38g. The radius of Mars is 2100 miles. Determine the velocity of a particle projected in a radial direction outward from Mars and acted upon by only the gravitational attraction of Mars by first modeling the motion into a differential equation and then solving the differential equation. Use your result to determine the velocity of escape from Mars.


Homework Equations


v^(2) = [2gR^(2) / r] + C


The Attempt at a Solution


g = 0.38
r = 2100 miles
R = ?
I don't understand the differential equation part at all. I'm confused because I'm only given 2 variables...

Any help is appreciated
 
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Your differential equation should consist of an expression that relates the acceleration experienced by the projectile with the distance.
 
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