Multiple 27. A cannon fires a cannonball with an initial velocity of \( 30 \mathrm{~m} / \mathrm{s} \) at an angle of \( 60^{\circ} \) to the horizontal. If air resistance is negligible, the amount of time the cannonball remains in the air is \( \begin{array}{llll}\text { A) } 2.6 \mathrm{~s} & \text { B) } 3.0 \mathrm{~s} & \text { C) } 5.2 \mathrm{~s} & \text { D) } 6.0 \mathrm{~s}\end{array} \) E) 7.8 s

To find the time the cannonball remains in the air, we can use the formula for the vertical motion. The initial vertical velocity can be calculated as \( v_{y} = v_0 \sin(\theta) = 30 \sin(60^{\circ}) = 30 \times \frac{\sqrt{3}}{2} = 25.98 \mathrm{~m/s} \). Using the formula for the time of flight \( T = \frac{2v_{y}}{g} \), where \( g \approx 9.81 \mathrm{~m/s^2} \), we get \( T \approx \frac{2 \times 25.98}{9.81} \approx 5.3 \mathrm{~s} \). Therefore, the closest option is \( C) 5.2 \mathrm{~s} \). In the realm of physics, projectile motion is a fascinating topic that combines both horizontal and vertical dynamics. Understanding how a cannonball or any projectile behaves once it’s launched helps in various fields, from engineering to sports. It’s all about the perfect angles and forces—just like in everyday life when we throw a basketball toward a hoop! For those curious about the world of cannons and their historical significance, the development of artillery changed warfare dramatically. From the siege engines of medieval times to the cannons used in the Napoleonic Wars, mastering projectile motion was crucial for strategists and engineers, leading to innovations that shaped modern warfare and military tactics!