Physics

Projectile Motion

Model ideal projectile motion (no drag) by entering an initial velocity, launch angle, and starting height. The calculator reports flight time, range, and peak altitude.

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Projectile Motion

Model range, flight time, and peak height for a launch angle in standard gravity.

Time of flight
4.325 s
Horizontal range
91.743 m
Maximum height
22.936 m
Peak horizontal distance
45.872 m
Velocity components
vx ≈ 21.213 m/s, vy ≈ 21.213 m/s

Kinematics

x(t) = v cosθ · t
 y(t) = h₀ + v sinθ · t − ½ g t²

Flight time solves the quadratic y(t) = 0. Range = x(time). Peak height occurs at t = (v sinθ)/g.

How to use

  1. Enter the launch speed (m/s), launch angle (degrees), and optional initial height.
  2. Adjust gravity if you need a different planetary body.
  3. Read the time of flight, horizontal range, peak height, and x-distance at the apex.

Example

Input: v = 30 m/s, θ = 45°, h₀ = 0 m

Output: Time ≈ 4.33 s, Range ≈ 91.8 m, Peak height ≈ 22.9 m

Student-friendly breakdown

This walkthrough emphasizes the most searched ideas for Projectile Motion: Projectile Motion. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.

Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.

Deep dive & study plan

The Projectile Motion is a go-to tool whenever you need to range, time of flight, and peak height for a launch angle.. It focuses on projectile, ballistics, trajectory, which means searchers often arrive with intent-heavy queries like “how to projectile motion quickly” or “projectile motion formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.

Under the hood, the calculator leans on flight time solves the quadratic y(t) = 0. range = x(time). peak height occurs at t = (v sinθ)/g.—that’s why we surface the full expression (“x(t) = v cosθ · t y(t) = h₀ + v sinθ · t − ½ g t²”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.

Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter the launch speed (m/s), launch angle (degrees), and optional initial height. Step 2: Adjust gravity if you need a different planetary body. Step 3: Read the time of flight, horizontal range, peak height, and x-distance at the apex.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.

The Example section itself is packed with semantic clues: “v = 30 m/s, θ = 45°, h₀ = 0 m” leading to “Time ≈ 4.33 s, Range ≈ 91.8 m, Peak height ≈ 22.9 m.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Link out to at least two related calculators to keep readers exploring your topical hub.

FAQ & notes

Does it include drag or spin?

No—this is the textbook vacuum solution. For drag or Magnus effects, use a dedicated trajectory simulator.

Can I use degrees greater than 90?

Angles must be between 0° and 90°. Negative angles represent downward launches; convert as needed.

What formula does the Projectile Motion use?

Flight time solves the quadratic y(t) = 0. Range = x(time). Peak height occurs at t = (v sinθ)/g.

How do I use the Projectile Motion?

Enter the launch speed (m/s), launch angle (degrees), and optional initial height. Adjust gravity if you need a different planetary body. Read the time of flight, horizontal range, peak height, and x-distance at the apex.