Range — Science definition

Defined in 2 courses:

The distance from the lowest value to the highest, which shows how consistent a set of measurements was. (Life Science & Scientific Inquiry)
The horizontal distance a projectile travels before returning to its launch height. (Physics & Environmental Science)

Where it is taught

Tables, Graphs & Patterns in Data — Scientific Inquiry & Diversity of Life, Life Science & Scientific Inquiry, Grade 7
Projectile & Two-Dimensional Motion — Motion & Kinematics, Physics & Environmental Science, Grade 12

In use

The range is the distance from the lowest to the highest, and it is the one people skip, which is a mistake, because a mean on its own hides everything about how spread out the measurements were.
Tables, Graphs & Patterns in Data

On level ground the range works out to R = v₀²sin(2θ) ÷ g, an expression that is largest when θ = 45°, because sin(2θ) reaches its maximum of 1 there.
Projectile & Two-Dimensional Motion

Questions using range

Problem 1

From 45 m height with horizontal speed 6 m/s and g=10, find flight time and range. Show the reasoning, not just the conclusion.

Hints

Solve vertical motion for time before using horizontal speed.

Answer and explanation

45=5t² gives t=3 s; range=18 m.

Problem 2

A ball is launched horizontally at 8.0 m/s from a 19.6 m ledge. Ignore drag and use g=9.8 m/s². Find flight time, horizontal range and landing velocity components.

Answer and explanation

0=19.6−4.9t² gives t=2.00 s. Range=8×2=16.0 m. Landing velocity=(8.0,−19.6) m/s in right/up-positive axes; speed≈21.2 m/s.

0=19.6−4.9t² gives t=2.00 s.

Range=8×2=16.0 m.

Landing velocity=(8.0,−19.6) m/s in right/up-positive axes; speed≈21.2 m/s.

Response criteria

Use the stated measurements or conditions, with correct units.
Connect the result to the physical or environmental mechanism or evidence relationship.
Identify the assumption, model limit or further evidence requested.

Problem 3

Independent chapter check: A ball is launched horizontally at 8.0 m/s from a 19.6 m ledge. Ignore drag and use g=9.8 m/s². Find flight time, horizontal range and landing velocity components.

Answer and explanation

0=19.6−4.9t² gives t=2.00 s. Range=8×2=16.0 m. Landing velocity=(8.0,−19.6) m/s in right/up-positive axes; speed≈21.2 m/s.

0=19.6−4.9t² gives t=2.00 s.

Range=8×2=16.0 m.

Landing velocity=(8.0,−19.6) m/s in right/up-positive axes; speed≈21.2 m/s.

Response criteria

Use the stated measurements or conditions, with correct units.
Connect the result to the physical or environmental mechanism or evidence relationship.
Identify the assumption, model limit or further evidence requested.

Taught alongside

Elsewhere

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