Q. A 10 kg ball is thrown vertically upward with an initial velocity of 15 \( \mathrm{~m} / \mathrm{s} \). Calculate the maximum height reached by the ball using the law of conservation of energy. Ignore air resistance.

To find the maximum height reached by the ball using the law of conservation of energy, we can equate the initial kinetic energy to the potential energy at the maximum height. The kinetic energy (KE) when the ball is thrown is given by: \[ KE = \frac{1}{2}mv^2 = \frac{1}{2}(10 \, \text{kg})(15 \, \text{m/s})^2 = \frac{1}{2}(10)(225) = 1125 \, \text{J} \] At the maximum height (h), all this kinetic energy is converted into gravitational potential energy (PE): \[ PE = mgh \] Setting KE equal to PE: \[ 1125 \, \text{J} = (10 \, \text{kg})(9.81 \, \text{m/s}^2)(h) \] Solving for h gives: \[ h = \frac{1125 \, \text{J}}{(10 \, \text{kg})(9.81 \, \text{m/s}^2)} \approx \frac{1125}{98.1} \approx 11.48 \, \text{m} \] So, the maximum height reached by the ball is approximately 11.48 meters. Did you know that the concept of conservation of energy dates back to the early 19th century? Scientists like Julius Robert von Meyer and Hermann von Helmholtz helped formalize it, showing how energy can neither be created nor destroyed, only transformed from one form to another. This principle laid the groundwork for modern physics and has applications in everything from roller coasters to rocket science! In real-world applications, engineers and architects rely on these principles when designing buildings and bridges. For example, when designing a roller coaster, understanding the transfer of energy between kinetic and potential forms is crucial for ensuring safety and excitement. An effective design maximizes thrills while ensuring that riders will safely return to ground level!