On the internet, a student finds the following equation for the time an object will take to fall to the ground from a height h, depending on the mass and radius of the planet the object is on t=√(2hG/MRP) Regardless of whether this equation is correct, does it agree with your qualitative reasoning in Parten In other words, does this equation for t have the expected dependence as reasoned in Part ?

a. Yes
b. NA

Question

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moya1316 moya1316 · Answer 1 · 2020-01-30T10:29:36+01:00

Answer:

t = √ ( 2h R² / GM)

This is the correct expression so we see the equation found is not correct

Explanation:

To answer this question, let's look for an expression for the time and fall of the body, using kinematics

v = vo + a t

v² = v₀² + 2 a h

Suppose the body is released, so its initial velocity is zero, when they reach the ground they have the speed

(at)² = 2 a h

t = √ 2h / a

To find acceleration, let's use Newton's second law, where force is the force of gravitation

F = m a

G m M / (R + h)² = m a

a = G M / (R + h)²

In general, if R >> h we can approximate the denominator expressions to R

a = G M / R²

Substituting

t = √ ( 2h R² / GM)

This is the correct expression so we see the equation found is not correct

Since the found equation is not correct, its dependence does not give units of time