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

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