Freefall Worksheet | PDF - Free Printable

Let's solve each problem step by step using the given equations:

- g = 9.81 m/s² (acceleration due to gravity)
- v = g × t (velocity after time t)
- d = ½ × g × t² (distance fallen in time t)

We will use correct significant figures and box our final answers.

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Problem 1:

> I drop a penny from the top of the tower at the front of Fort Collins High School and it takes 1.85 seconds to hit the ground. Calculate the velocity in m/s after 1.10 seconds of freefall and calculate the velocity at impact in mi/hr.

#### Part A: Velocity after 1.10 seconds
Use:
$$ v = g \cdot t $$
$$ v = 9.81 \, \text{m/s}^2 \times 1.10 \, \text{s} = 10.791 \, \text{m/s} $$

Significant figures: 1.10 has 3 sig figs → round to 10.8 m/s

✔ Answer: 10.8 m/s

#### Part B: Velocity at impact (after 1.85 s)
$$ v = 9.81 \times 1.85 = 18.1385 \, \text{m/s} $$

Round to 3 sig figs (1.85 has 3): 18.1 m/s

Now convert to mi/hr:

We know:
- 1 m/s ≈ 2.23694 mi/hr

So:
$$ 18.1 \, \text{m/s} \times 2.23694 \approx 40.43 \, \text{mi/hr} $$

Round to 3 sig figs: 40.4 mi/hr

✔ Answer: 40.4 mi/hr

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Problem 2:

> If I drop a watermelon from the top of one of the tower dorms at CSU, and it takes 3.44 seconds to hit the ground, calculate how tall the building is in meters and then convert into feet.

Use:
$$ d = \frac{1}{2} g t^2 $$

$$ d = 0.5 \times 9.81 \times (3.44)^2 $$

First compute $ t^2 $:
$ 3.44^2 = 11.8336 $

Then:
$$ d = 0.5 \times 9.81 \times 11.8336 = 4.905 \times 11.8336 \approx 58.04 \, \text{m} $$

Time (3.44 s) has 3 sig figs → round to 58.0 m

Now convert to feet:
1 meter ≈ 3.28084 feet
$$ 58.0 \times 3.28084 \approx 190.0 \, \text{ft} $$

Round to 3 sig figs: 190 ft

✔ Answer: 58.0 m, 190 ft

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Problem 3:

> You are walking in Paris alongside the Eiffel Tower and suddenly a croissant smacks you on the head and knocks you to the ground. From your handy dandy tourist guidebook you find that the height of the Eiffel Tower is 300.5 m. If you neglect air resistance, calculate how many seconds the croissant dropped before it tagged you on the head.

Use:
$$ d = \frac{1}{2} g t^2 $$

Solve for $ t $:
$$ t = \sqrt{\frac{2d}{g}} $$

Plug in:
$$ t = \sqrt{\frac{2 \times 300.5}{9.81}} = \sqrt{\frac{601.0}{9.81}} = \sqrt{61.26} \approx 7.827 \, \text{s} $$

Height (300.5 m) has 4 sig figs, so answer should have 4 sig figs? But let’s check:

- 300.5 → 4 sig figs
- g = 9.81 → 3 sig figs → limiting factor

So round to 3 sig figs: 7.83 s

✔ Answer: 7.83 s

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Problem 4:

> During the latter part of your European vacation, you are hanging out at the beach at the gold coast of Spain. As you are laying in your chaise lounge soaking up the warm Mediterranean sun, a large glob of seagull poop hits you in the face. Since you got an "A" in ICPE you are able to estimate the impact velocity at 98.5 m/s. Neglecting air resistance, calculate how high up the seagull was flying when it pooped.

Use:
$$ v = g t \Rightarrow t = \frac{v}{g} $$

But we want height: use
$$ v^2 = 2gd \Rightarrow d = \frac{v^2}{2g} $$

$$ d = \frac{(98.5)^2}{2 \times 9.81} = \frac{9702.25}{19.62} \approx 494.5 \, \text{m} $$

Velocity (98.5 m/s) has 3 sig figs → round to 495 m

✔ Answer: 495 m

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Problem 5:

> If you were to throw a large log over the edge of the Grand Canyon and it took 5.65 seconds to hit the ground, calculate the velocity of the log at impact in m/s and calculate the distance the log fell in feet.

#### Part A: Velocity at impact
$$ v = g \cdot t = 9.81 \times 5.65 = 55.4165 \, \text{m/s} $$

Round to 3 sig figs (5.65 has 3): 55.4 m/s

✔ Answer: 55.4 m/s

#### Part B: Distance fallen in feet

First, find distance in meters:
$$ d = \frac{1}{2} g t^2 = 0.5 \times 9.81 \times (5.65)^2 $$

$ 5.65^2 = 31.9225 $

$$ d = 4.905 \times 31.9225 \approx 156.6 \, \text{m} $$

Convert to feet:
$ 156.6 \times 3.28084 \approx 513.8 \, \text{ft} $

Round to 3 sig figs: 514 ft

✔ Answer: 514 ft

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## ✔ Final Answers Boxed:

1.
- Velocity after 1.10 s: $\boxed{10.8\ \text{m/s}}$
- Velocity at impact: $\boxed{40.4\ \text{mi/hr}}$

2.
- Height: $\boxed{58.0\ \text{m}}$, $\boxed{190\ \text{ft}}$

3.
- Time: $\boxed{7.83\ \text{s}}$

4.
- Height: $\boxed{495\ \text{m}}$

5.
- Impact velocity: $\boxed{55.4\ \text{m/s}}$
- Distance: $\boxed{514\ \text{ft}}$

Let me know if you'd like these formatted as a printable worksheet!