Final answer:
To find how long it takes for the thrown ball to hit the ground, solve the quadratic equation 0 = -16t² - 20t + 280 for the positive value of t, as time cannot be negative. This solution will give the time in seconds.
Step-by-step explanation:
To determine how long it will take for the ball to hit the ground when thrown vertically from a tall building, we need to find when the height h(t) is zero using the given quadratic equation:
h(t) = -16t² - 20t + 280.
We need to find the positive value of t that makes h(t) equal to zero, which represents the time after the ball is thrown when it hits the ground. Using the quadratic formula, t can be found by solving the equation 0 = -16t² - 20t + 280. After calculating, we would get two solutions for t, and we are only interested in the positive value, as time cannot be negative. The exact solution that yields a result in the positive seconds would be accepted as the time it takes for the ball to hit the ground.
In general scenarios for projectile motion, the time for an object to hit the ground is determined completely by its vertical motion.