Free Fall Problems- Example Solutions
Free Fall Problems: The No-Nonsense Guide to Solving Them
Free fall problems are the backbone of physics homework and exams. Most students either overthink them or rush through them. Here's how to actually solve them correctly.
What Is Free Fall?
Free fall is when an object moves under gravity alone. No air resistance. No push. Just the pull of Earth's gravity accelerating it downward.
The acceleration is constant: g = 9.8 m/s² (or 32 ft/s² if you're using imperial units). This value never changes for objects near Earth's surface.
Direction matters. If you define down as positive, your velocity and acceleration are positive. If you define up as positive, acceleration is negative. Pick one direction and stick with it.
The Equations You Actually Need
Four kinematic equations. You'll probably only need two for most problems.
- v = v₀ + at — velocity equals initial velocity plus acceleration times time
- d = v₀t + ½at² — displacement from initial velocity and time
- v² = v₀² + 2ad — velocity squared relation
- d = ½(v₀ + v)t — average velocity times time
For free fall, substitute a = g. That's it.
Example Problem 1: Dropping From Rest
You drop a ball from a 45-meter tall building. How long does it take to hit the ground?
Step 1: Identify knowns.
- d = 45 m (downward)
- v₀ = 0 m/s (dropped, not thrown)
- g = 9.8 m/s²
- t = ?
Step 2: Pick your equation.
Since we need time and we know displacement, initial velocity, and acceleration, use d = v₀t + ½at².
Step 3: Plug in and solve.
45 = 0(t) + ½(9.8)t²
45 = 4.9t²
t² = 9.18
t = 3.03 seconds
That's your answer. No fancy steps required.
Example Problem 2: Thrown Downward
A rock is thrown downward from a cliff at 12 m/s. It hits the water below in 2.5 seconds. How tall is the cliff?
Step 1: Identify knowns.
- v₀ = 12 m/s (downward = positive)
- t = 2.5 s
- g = 9.8 m/s²
- d = ?
Step 2: Use d = v₀t + ½at²
d = (12)(2.5) + ½(9.8)(2.5)²
d = 30 + 4.9(6.25)
d = 30 + 30.6
d = 60.6 meters
The cliff is about 61 meters tall.
Example Problem 3: Thrown Upward
You throw a ball straight up at 20 m/s. How high does it go?
Step 1: Identify knowns.
- v₀ = 20 m/s (upward = positive)
- v = 0 m/s (at the top, velocity is zero)
- g = -9.8 m/s² (acceleration is always downward)
- d = ?
Step 2: Pick the equation without time.
v² = v₀² + 2ad
Step 3: Solve.
0² = (20)² + 2(-9.8)d
0 = 400 - 19.6d
19.6d = 400
d = 20.4 meters
Sign Convention: Where Students Lose Points
Most free fall mistakes come from inconsistent signs. Here's the rule:
- If you define up as positive, then g = -9.8 m/s²
- If you define down as positive, then g = +9.8 m/s²
You can use either. Just be consistent throughout the entire problem. Mixing signs will always give you the wrong answer.
Quick Reference: g Values in Different Units
| Location | Value | Units |
|---|---|---|
| Earth (standard) | 9.8 | m/s² |
| Earth (standard) | 32 | ft/s² |
| Moon | 1.62 | m/s² |
| Mars | 3.71 | m/s² |
Use 9.8 unless your teacher specifies otherwise. Some textbooks use 10 for simplicity—check your assignment.
Getting Started: Step-by-Step Process
Before you write anything down:
- Read the problem twice. Know what's being asked before you grab an equation.
- List your knowns. v₀, v, a, t, d—whatever's given.
- Choose a sign convention. Up or down, positive or negative. Write it at the top of your work.
- Pick the equation that fits. You need three knowns to solve for the fourth.
- Solve algebraically first. Plug in numbers only after you isolate the variable.
- Check your units. If you get a negative time or impossible height, something's wrong with your signs.
Common Mistakes That Kill Your Grade
- Using g = 10 when the problem expects 9.8. Check your instructions.
- Forgetting that velocity at the top of a throw is zero. Not the velocity—it's zero.
- Mixing up displacement and height. Displacement is net change. Height above starting point is different.
- Not converting units. Meters and centimeters. Seconds and minutes. Sort it out before you calculate.
The Bottom Line
Free fall problems are straightforward once you stop overcomplicating them. Four equations. One acceleration value. Consistent signs. That's all you need.
Practice the three example problems above until you can solve them without checking the solutions. If you can do that, you're ready for any free fall problem your teacher throws at you.