Projectile Motion: Range, Time of Flight and Max Height
Break launch velocity into components and find time of flight, range and maximum height for a projectile, with two worked physics examples.
Split the launch velocity
- vₓ = v cos θ (constant)
- v_y = v sin θ (changes by g)
Horizontal and vertical motion are independent.
KEY FORMULAS (g = 9.8 m/s²)
- Time of flight = 2 v sin θ / g
- Range = v² sin 2θ / g
- Max height = (v sin θ)² / 2g
These assume launch and landing at the same height.
Example 1
A ball is launched at 20 m/s at 30°. Find the time in the air.
- v sin θ = 20(0.5) = 10 m/s
- Time = 2(10) / 9.8
≈ 2.04 s
Example 2
For the same launch, find the maximum height.
- (v sin θ)² = 10² = 100
- Max height = 100 / (2 × 9.8)
≈ 5.1 m
Common mistake
Vertical speed is zero the whole flight
Only at the top of the path is vertical velocity zero.
Horizontal velocity stays constant (no air resistance).
Use sin for vertical and cos for horizontal.
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