Motion in Two Dimensions, Component by Component

You'll learnto differentiate a position vector component by component to solve a full projectile problem.

Position is a vector function of time. Differentiate it component by component — the unit vectors just ride along — and a full projectile problem falls out of two one-dimensional motions that share nothing but the clock.

8 STEPS · 6 QUICK CHECKS · v3

VECTOR KINEMATICS LAB

Before you start

What you're looking at

A projectile launched from the origin at 20 m/s, 30° above horizontal, its flight path previewed over level ground.

The question

What is the velocity vector at the peak, and how far downrange does the ball land?

Watch for

Don't assume velocity is zero at the top; position r(t) is differentiated one component at a time.

What the symbols mean

Blue arrow is the î (horizontal) piece, amber arrow the ĵ (vertical) piece; origin is the launch point, g = 10 m/s².

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