LearnViz Math
Advanced ∿ Trigonometry Topic 90 of 98

Range of a Projectile

Horizontal distance depends on launch angle.

Key idea

Horizontal distance depends on launch angle.

In depth

A projectile launched at speed v and angle θ travels R = v² sin 2θ / g on level ground. The maximum is at 45°, and complementary angles such as 30° and 60° give the same range.

Worked example

v = 20 m/s, θ = 30°: R = 400 × 0.866/9.8 ≈ 35.3 m.

Formula

R = v² sin2θ / g

Real-world uses

Common mistake

Using θ directly rather than 2θ in the sine.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Range of a Projectile?

Horizontal distance depends on launch angle. It is a topic at the advanced level in Trigonometry.

What is the formula for Range of a Projectile?

The key formula is R = v² sin2θ / g.

Where is Range of a Projectile used in real life?

Real-world examples: Choosing the best launch angle in sports such as basketball, golf and javelin.

What should I learn before Range of a Projectile?

Make sure you are comfortable with Snell’s Law, the previous topic in Trigonometry.

What is a common mistake with Range of a Projectile?

Using θ directly rather than 2θ in the sine.

How can I practise Range of a Projectile?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Range of a Projectile?

Move on to Product of Trig Values next.

Related advanced topics in Trigonometry