Maximum height in projectile motion is \( H = \frac{u_y^2}{2g} \), where \( u_y \) is vertical velocity.
The maximum height of the projectile is determined using its initial vertical velocity and the standard projectile motion formula for maximum height. The initial vertical velocity component is calculated via the sine function: \( v_{0y} = v_0 \sin \theta = 20 \, \text{m/s} \times \sin 30^\circ \). Given that \( \sin 30^\circ = 0.5 \), the initial vertical velocity is: \( v_{0y} = 20 \times 0.5 = 10 \, \text{m/s} \). The maximum height formula is \( h = \frac{{v_{0y}^2}}{2g} \). Substituting \( v_{0y} = 10 \, \text{m/s} \) and \( g = 10 \, \text{m/s}^2 \) yields: \( h = \frac{{10^2}}{2 \times 10} = \frac{100}{20} = 5 \, \text{m} \). Therefore, the projectile reaches a maximum height of \( 5 \, \text{m} \).
A solid metallic cube having total surface area $ 24 \, \text{m}^2 $ is uniformly heated. If its temperature is increased by $ 10^\circ \, \text{C} $, calculate the increase in volume of the cube.
$ \text{(Given: } \alpha = 5.0 \times 10^{-4} \, \text{C}^{-1} \text{)} $