Projectile Motion at an Angle
PhysicsKinematicsAges 15–16Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Kinematics
Launch an object with initial speed v0 at angle α to the horizontal, under gravitational acceleration g. Watch the trajectory, the range L = v0²·sin(2α)/g, the maximum height, and the time of flight. Press Fire to run again.
Lesson: Projectile motion, horizontal projectile motion
What it shows
A projectile launched at an angle moves in two independent directions at once: horizontally at constant speed v0·cos α, and vertically with constant downward acceleration g, starting at v0·sin α. Combining the two gives a parabolic path. With air resistance ignored and launch and landing at the same height, the time of flight is T = 2v0·sin α/g, the maximum height is H = v0²·sin²α/(2g) and the range is L = v0²·sin(2α)/g. The range is greatest at 45°, and complementary angles such as 30° and 60° give the same range.
How to use
Keep Initial speed fixed and fire at several values of Launch angle, noting the range, maximum height and time of flight from the readout each time. Compare 30° with 60° and look for the angle that gives the longest range. Then double the Initial speed to see how range and height scale, and lower Gravitational acceleration to 1.6 m/s², the value on the Moon. Press Fire after each change to launch again.
Parameters you can change
- Initial speed 5–50 m/s
- Launch angle 5–85 deg
- Gravitational acceleration 1–25 m/s²
Questions to explore
- Why do launch angles of 30° and 60° give the same range but different flight times?
- When the initial speed doubles, by what factor do the range and the maximum height change?
- Is the projectile's velocity zero at the top of its path? What does the velocity arrow show there?
