01 Key Concepts
Projectile Motion Setup
Combines constant horizontal velocity (no horizontal acceleration) with constant vertical acceleration due to gravity (g ≈ 9.8 m/s^2 downward).
Horizontal Motion
Since there's no horizontal force (ignoring air resistance), horizontal velocity stays constant throughout the flight: x = vx*t.
Vertical Motion
Vertical velocity changes due to gravity: vy = vy0 - g*t, and vertical position follows y = vy0*t - (1/2)*g*t^2.
Time of Flight
For a projectile launched and landing at the same height, time of flight = 2*vy0/g.
Maximum Height and Range
Maximum height = vy0^2/(2g). Range (horizontal distance) = vx*(time of flight), often written as R = v^2*sin(2*theta)/g for launch speed v and angle theta.
02 Key Formulas
- Time of flight (same launch/landing height) = 2*vy0/g
- Maximum height = vy0^2 / (2g)
- Range = v^2 * sin(2*theta) / g
03 Solved Examples
Example 1 A ball is thrown horizontally at 10 m/s from a height where it takes 2 seconds to hit the ground. Find the horizontal distance traveled.
- Horizontal velocity stays constant: x = vx*t = 10*2.
Answer: 20 meters
Example 2 A projectile is launched straight up at 20 m/s (g=10 m/s^2). Find the time to reach maximum height.
- At maximum height, vertical velocity = 0.
- Using vy=vy0-g*t: 0 = 20-10t, so t=20/10.
Answer: 2 seconds
Example 3 A projectile is launched at 30 m/s at a 45° angle (g=10 m/s^2, sin(90°)=1). Find its range.
- Apply R = v^2*sin(2*theta)/g = 30^2*sin(90°)/10.
- = 900*1/10.
Answer: 90 meters
04 Practice Questions
1A ball is thrown horizontally at 5 m/s and falls for 3s. Find horizontal distance.
15 m
2A projectile is launched straight up at 30 m/s (g=10). Find time to max height.
3s
3Find the max height for vy0=20 m/s (g=10).
20 m (using vy0^2/(2g)=400/20)
4What is the horizontal acceleration of a projectile (ignoring air resistance)?
0 (horizontal velocity stays constant)
5What is the approximate value of g used in these problems?
9.8 m/s^2 (or approximated as 10 m/s^2)
📄 Projectile Motion — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.