A skydiver drops her watch as she jumps out of a plane flying at an altitude of 6,400 feet. If the equation for height as a function of time is \( h(t)=-16 \mathrm{t}^{2}+ \) initial height where \( t \) is time in secondst and \( h(t) \) is height in feet, how many seconds will it take for the watch to hit the ground? [? ] seconds

To find out how long it takes for the watch to hit the ground, we need to set \( h(t) = 0 \) and solve the equation. Given that the initial height is 6,400 feet, our equation becomes \( 0 = -16t^2 + 6400 \). Rearranging gives us \( 16t^2 = 6400 \), or \( t^2 = 400 \). Taking the square root gives us \( t = 20 \). So, it will take 20 seconds for the watch to hit the ground! In the thrilling world of skydiving, objects in free fall experience acceleration due to gravity, which is about 32 feet per second squared in the U.S. customary system. Interestingly, skydivers themselves reach terminal velocity, slowing their descent to about 120 miles per hour, or roughly 176 feet per second, once air resistance balances the force of gravity! To better understand the effects of air resistance, you might want to explore how different shapes and masses affect the fall of objects. A feather gently floats down, while a rock plummets at a different rate! This concept can help you grasp how various materials respond to gravity and the environment on earth.