Gravity: Model Vertical Free Fall

Use constant-acceleration equations with a clear sign convention.

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Near a surface, model g as constant and ignore air resistance. From rest, downward speed v = gt and downward distance s = gt^2/2. If upward is positive, acceleration is -g, including at the top of an upward toss.

Worked example

With g = 10 m/s^2, an object dropped from rest falls 20 m in 2 s and reaches a downward speed of 20 m/s. This is a calculation model, not an instruction to drop objects from buildings.

Two objects of different mass start at the same height and at rest in a uniform gravitational field with no air. Matching arrows and final positions represent equal acceleration and landing time.

Would you believe it?

On Apollo 15, a hammer and a feather released together reached the Moon surface together. Essentially no air was there to slow the feather.

NASA: the hammer and feather

Question 1 At g = 10 m/s^2, what is downward speed after 3 s from rest? 30 m/s 45 m/s 90 m/s

Question 2 In the same model, how far does it fall in 3 s? 30 m 90 m 45 m

Question 3 A ball starts upward at 20 m/s. When does it first reach zero vertical speed? 0.5 s 2 s 20 s

Question 4 At that highest point, what is its acceleration with upward positive? -10 m/s^2 0 m/s^2 +10 m/s^2

Question 5 Which effect makes this constant-g, no-drag model less accurate for a real falling leaf? Writing time in seconds The existence of gravity Air resistance

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