What is Projectile Motion?
Projectile motion describes the curved path of an object launched into the air, like a thrown ball or a cannonball. It combines constant horizontal velocity with vertical motion under gravity, producing a parabolic trajectory.
Projectile motion is two-dimensional motion where an object moves horizontally at constant velocity while accelerating downward due to gravity, tracing a parabola. Its range is R = v²sin(2θ)/g.
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Step-by-step worked examples
A ball is launched at 20 m/s at a 30° angle. Find its range (g = 9.8 m/s²).
R = v²sin(2θ)/g R = 20² × sin(60°) / 9.8 R = 400 × 0.866 / 9.8 R = 35.35 m
A projectile is launched at 15 m/s at 45°. Find its time of flight.
T = 2v·sinθ / g T = 2 × 15 × sin(45°) / 9.8 T = 21.21 / 9.8 T = 2.16 s
A projectile is launched at 25 m/s at 60°. Find its maximum height.
H = v²sin²θ / (2g) H = 25² × sin²(60°) / (2 × 9.8) H = 625 × 0.75 / 19.6 H = 23.92 m
Flashcards
Quick quiz
Q1.At what launch angle is the range of a projectile maximized (level ground)?
Q2.What happens to horizontal velocity during projectile motion (no air resistance)?
Q3.A ball launched at 10 m/s and 45° has what approximate range (g = 9.8 m/s²)?
Q4.What causes the parabolic shape of projectile motion?
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Common mistakes
Assuming horizontal and vertical motions affect each other. — Correct: They're independent — gravity only acts vertically; horizontal velocity stays constant.
Using the same equations for vertical and horizontal motion. — Correct: Horizontal: x = v·cosθ·t (no acceleration). Vertical: y = v·sinθ·t − ½g·t² (constant acceleration g).
Believing maximum range always occurs at the highest angle. — Correct: Maximum range is at 45°, not 90° (which gives zero range on level ground).
Forgetting units when angle is given in degrees vs radians. — Correct: Convert to the correct unit consistently — most projectile formulas expect angle in degrees or convert to radians for trig functions.
FAQ
What is projectile motion?
It's the curved, parabolic path of an object launched into the air, resulting from constant horizontal velocity and gravity's vertical pull.
What is the formula for projectile motion range?
R = v²sin(2θ)/g, where v is initial speed, θ is launch angle, and g is gravitational acceleration.
How do you calculate projectile motion with an example?
For v = 20 m/s at 30°: R = 20² × sin(60°) / 9.8 = 35.35 m. Break the motion into horizontal and vertical components.
What are real-world examples of projectile motion?
A thrown basketball, a kicked football, water from a fountain, and a cannonball all follow projectile motion paths.