projectile motion (range)

Question

A projectile is launched with speed 20 m/s at 30° above horizontal. Ignore air resistance. What is its range? (g = 10 m/s²)

RankGuru · Accepted Answer

1. **Identify Projectile Variables**:
   - Initial speed ($u$) $= 20$ m/s
   - Angle ($	heta$) $= 30^\circ$
   - Acceleration ($g$) $= 10 	ext{ m/s}^2$
2. **Range Formula**: Horizontal range $R = \frac{u^2 \sin(2	heta)}{g}$.
3. **Calculate Trigonometric term**: $\sin(2 	imes 30^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$.
4. **Numerical Substitution**:
   - $R = \frac{20^2 	imes 0.866}{10}$
   - $R = \frac{400 	imes 0.866}{10} = 40 	imes 0.866 = 34.64$ m.
5. **Final Result**: The range is approximately **$34.6$ m**.

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projectile motion (range)

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