Question

The height of an object after it is released can be modeled by the function f (x) = negative 16 t squared + v t + s, where t is the number of seconds after the object is released, v is the upward speed in feet per second at release, and s is the starting height in feet. If a quarterback throws a ball from his hand 6 feet in the air at an upward speed of 25 feet per second, how much time does his teammate have to catch the ball?
about 1.45 seconds
about 1.77 seconds
about 3 seconds
about 6 seconds

Answer 1

We set -16t^2 + 25t + 6 = 0 (time when the ball hits the ground). Solve with the quadratic formula:

t = [25 ± sqrt(25^2 + 4·16·6)] / (2·16) = [25 ± sqrt(1009)] / 32.

sqrt(1009) ≈ 31.768, so the positive root is t ≈ (25 + 31.768)/32 ≈ 1.77 s.

Answer: about 1.77 seconds.