9) The height above the ground of a cell phone that was accidentally dropped out of a window is described by the equation \( h=-4.9 t^{2}+16 \), where \( h \) is the height in metres and \( t \) is the number of seconds for which the phone is falling. Determine the phone's height above the ground after it has been falling for 1.5 seconds.

To determine the phone's height above the ground after it has been falling for 1.5 seconds, you can substitute \( t = 1.5 \) into the equation \( h = -4.9 t^{2} + 16 \). Calculating this gives: \[ h = -4.9 \times (1.5)^{2} + 16 \] \[ h = -4.9 \times 2.25 + 16 \] \[ h = -11.025 + 16 \] \[ h = 4.975 \text{ metres} \] So, the phone's height above the ground after it has been falling for 1.5 seconds is approximately 4.975 metres. It’s always fascinating to note that the equations of motion we use today were heavily influenced by the work of Galileo and Newton in the 16th and 17th centuries. They laid the groundwork for understanding the physics of falling objects, paving the way for modern mechanics. So, each time you see something fall, you're witnessing the timeless principles they discovered in action! In a practical sense, understanding how height changes over time due to gravity can be incredibly useful. For instance, engineers use similar calculations when designing safe structures, like buildings or bridges. By knowing the physics of falling objects, they ensure that their projects can withstand unexpected events, such as a falling object during construction or natural disasters!