Derive equation for a freely falling particles velocity

[mathwizeguy]

Homework Statement

Derive an equation that relates the velocity of a freely falling particle to its altitude. Assume that the particle is released from rest at an altitude from the Earth's surface.

Express your answer in terms of the variables and , constant gravitational acceleration at sea level , and the radius of the Earth .

Homework Equations

Given Equation :a=-g*[R^2/(R+y)^2]
R=radius of the earth.

The Attempt at a Solution

i tried taking the second derivative and used the chain rule but i got a different answer from what was shown.

 

[Redbelly98]

Homework Statement

Derive an equation that relates the velocity of a freely falling particle to its altitude. Assume that the particle is released from rest at an altitude from the Earth's surface.

Express your answer in terms of the variables and , constant gravitational acceleration at sea level , and the radius of the Earth .

Homework Equations

Given Equation :a=-g*[R^2/(R+y)^2]
R=radius of the earth.

The Attempt at a Solution

i tried taking the second derivative and used the chain rule but i got a different answer from what was shown.

What, specifically, has your class been studying lately? Would it by any chance have something to do with work, kinetic energy, potential energy, and stuff like that?