Projectile Range

Projectile Motion

When an object is launched at speed $v_0$ and angle $\theta$ above horizontal (ignoring air resistance), it follows a parabolic path. Horizontal and vertical motion are independent.

Horizontal Range

The total horizontal distance (range) when landing at the same height:

$R = \frac{v_0^2 \sin(2\theta)}{g}$

Maximum Height

$h_{\max} = \frac{v_0^2 \sin^2(\theta)}{2g}$

Key Observations

• 45° gives maximum range: $\sin(2 \times 45°) = \sin(90°) = 1$
• Complementary angles have equal range: 30° and 60° give the same $R$
• Range scales as $v_0^2$ — doubling launch speed quadruples range

Examples at $v_0 = 20$ m/s

Your Task

Implement projectileRange(v0, angle_deg) returning range in metres.

Hint: Convert degrees to radians: $\text{angle\_rad} = \text{angle\_deg} \times \pi / 180$.