AP Physics 1 · Unit 1 · Topic 8 of 8 · 6 min lesson

Projectile Motion

A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.

Quiz this topic · 5 questions Watch the review video ↗

The big idea

A projectile is two motions at once. Sideways, it moves at a constant velocity (no horizontal acceleration). Up and down, it’s in free fall, with a = 10 m/s² downward. Time is the one thing they share.

1. Two motions in one

Dots at equal time steps: equal steps sideways, bigger and bigger steps down.

Gravity pulls straight down, so it only changes the vertical part of the velocity. Nothing pushes sideways (ignoring air resistance), so the horizontal part never changes.

That’s why a ball launched sideways and a ball dropped at the same moment hit the floor at the same time: their vertical motions are identical.

2. Two charts, one time

Horizontal: a_x = 0v_x stays constant

Δx = v_xthorizontal distance

Vertical: a_y = −10 m/s²up = +

v_y = v_0y + a_yt, …the free-fall equations

Make one chart for x and one for y. Solve whichever one gives you the time, then use that time in the other.

Launched at an angle θ? Split the launch speed first: v_0x = v₀ cos θ and v_0y = v₀ sin θ.

At the top of the path, v_y = 0, but v_x is unchanged, so the speed there is v_x, not zero.

3. Example, then try it

Example

A ball rolls off a 20 m cliff at 15 m/s. How long is it in the air, and how far from the cliff does it land?

Vertical (up = +): v_0y = 0, a_y = −10 m/s², Δy = −20 m. Δy = ½a_yt² → −20 = −5t² → t = 2.0 s

Horizontal: Δx = v_xt = 15 × 2.0 = 30 m

Try it · work it on paper first

A ball is launched from the ground at 20 m/s, 37° above horizontal, and lands at the same height. Find its maximum height and its range. (cos 37° ≈ 0.80, sin 37° ≈ 0.60)

Split the launch velocity: v_0x = 20(0.80) = 16 m/s; v_0y = 20(0.60) = 12 m/s.

Time to the top (v_y = 0): 0 = 12 − 10t → t = 1.2 s.

Max height: v_y² = v_0y² + 2a_yΔy → 0 = 144 − 20Δy → Δy = 7.2 m

Range: it lands at the same height, so total time = 2 × 1.2 = 2.4 s. Δx = 16 × 2.4 = 38.4 m

Answer: maximum height 7.2 m; range about 38 m.

4. Common mistakes

“The velocity is zero at the top.”Only v_y is zero. The ball is still moving sideways at v_x.

“The horizontal velocity slows down.”Without air resistance, nothing acts sideways, so v_x stays the same the whole flight.

Mixing directions.Using the full 20 m/s in the vertical chart, or g in the horizontal chart. Each chart gets only its own components.

Check yourself

At the same instant, one ball is dropped from a table and another is launched horizontally off the same table at 5 m/s. Which hits the floor first?

Both start with zero vertical velocity and have the same downward acceleration, so they fall the same height in the same time. The launched ball just lands farther away.

Ready to practice?

5 questions on Projectile Motion, each with a hint and an explanation for every wrong answer.

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