Calculate \( \sin(60^\circ) \approx 0.866 \).

February 22, 2026

$Calculate \( \sin(60^\circ) \approx 0.866 \).$

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A projectile is launched with an initial velocity of 50 m/s at an angle of 30 degrees above the horizontal. Calculate the horizontal range of the projectile, assuming no air resistance and using \( g = 9.8 \, \text{m/s}^2 \).
The formula for the range \( R \) is \( R = \frac{v^2 \sin(2\theta)}{g} \).
\( v = 50 \, \text{m/s} \), \( \theta = 30^\circ \), and \( g = 9.8 \, \text{m/s}^2 \).
Substitute the values: \( R = \frac{50^2 \times 0.866}{9.8} \).
Calculate \( 50^2 = 2500 \).
Multiply: \( 2500 \times 0.866 = 2165 \).

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