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Let the width be \( w \). Then the length is \( 3w \). The perimeter is given by:
The length is \( 3 \times 8 = 24 \, \text{m} \). The area is:
\[ \text{Area} = w \times \text{length} = 8 \times 24 = 192 \, \text{m}^2 \]
A projectile is launched with an initial velocity of 50 m/s at an angle of 30 degrees to the horizontal. What is the horizontal range of the projectile? (Assume no air resistance and \( g = 9.8 \, \text{m/s}^2 \))
The horizontal range \( R \) is given by:
\[ R = \frac{v^2 \sin(2\theta)}{g} \]
\[ R = \frac{50^2 \sin(60^\circ)}{9.8} \]
\[ R = \frac{2500 \times \frac{\sqrt{3}}{2}}{9.8} \]
\[ R \approx \frac{2500 \times 0.866}{9.8} \]
\[ R \approx \frac{2165}{9.8} \approx 220.92 \, \text{m} \]