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30 September, 04:26

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

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Answers (1)
  1. 30 September, 07:57
    0
    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
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