Question

A tourist in a sightseeing balloon drops his cell phone from a height of 880 feet above the ground (see picture). Find the time t (in seconds) for the object to reach the ground. The height (above ground) of the object is modeled by_______

Answer 1

The height of the object is modeled by a quadratic equation.

Step-by-step explanation:

The equation is obtained by considering the initial height of 880 feet, the acceleration due to gravity (32.2 feet per second squared), and the fact that the final position is 10 feet above the ground. The equation is:

h(t) = -16t² + 880

To find the time it takes for the object to reach the ground, we need to solve the equation h(t) = 0. Using the quadratic formula, we get two solutions: t = 3.79 seconds and t = 0.54 seconds. Since the ball is at a height of 10 feet at two times during its trajectory, we take the longer solution, which is t = 3.79 seconds.