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Physics · Class 11

Projectile trajectory

Motion in a Plane

Resolve the launch velocity into horizontal and vertical components. With no air resistance, horizontal velocity stays constant while vertical velocity decreases by g each second. At the apex the vertical velocity is zero; horizontal velocity usually remains. The ball follows a parabola until ground contact.

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Gravity changes the vertical motion.

காற்றுத் தடை இல்லாவிட்டால் கிடைமட்ட வேகம் மாறாது. ஈர்ப்பு விசையால் செங்குத்து வேகம் மாறுகிறது. உச்சியில் செங்குத்து வேகம் மட்டும் பூஜ்யம்; கிடைமட்ட வேகம் பொதுவாகத் தொடரும்.

Key notes, relationships and model limits

Key relationship

x = (u cosθ)t; y = h + (u sinθ)t − ½gt²; vₓ = u cosθ; vᵧ = u sinθ − gt; T = [u sinθ + √((u sinθ)² + 2gh)] / g.

Remember

Resolve the launch velocity into horizontal and vertical components. With no air resistance, horizontal velocity stays constant while vertical velocity decreases by g each second. At the apex the vertical velocity is zero; horizontal velocity usually remains. The ball follows a parabola until ground contact.

Common trap

At the highest point, velocity is not generally zero. Only its vertical component is zero; acceleration is still downward.

Model limits

Point particle; constant downward g; no air drag; flat ground y=0. Motion stops at the first ground contact; landing velocity is set to zero and no rebound is modelled. Range and peak height refer to ideal flight. Slider changes recompute a launch, and presets or Reset relaunch at t=0. The 22 s clock covers every allowed launch.

What you will learn

Connect trajectory and velocity components; calculate flight time, range and peak; distinguish horizontal and vertical launches.

Try the experiment

Play, pause near the apex, and inspect the two velocity components. Compare 30° and 60° launches, then try a ledge or a vertical launch. Reset or a preset starts another launch.

Think of it this way

A ball thrown across a room keeps moving sideways while gravity pulls it downward throughout the journey.

Worked example

For u=20 m/s, θ=45°, h=0 and g=9.81 m/s²: T≈2.883 s, R≈40.775 m, H≈10.194 m. R=u² sin2θ/g applies only when launch and landing heights agree.

Why this matters

The same time links the two motions. Equal launch and landing heights give complementary angles equal ranges, but different flight times and peaks.

Before you start

Rectangular axes · Pythagoras · sine and cosine

Check your understanding

For an oblique projectile with no air drag, what is zero at the apex?

Read the explanation

Vertical velocity is zero momentarily. Horizontal velocity is constant and acceleration remains (0,−g). A purely vertical launch is a special case with vₓ=0 throughout.

Course connection: CBSE XI Motion in a Plane; NEET/JEE kinematics. Use the assumptions stated in each question.