The height of an object after it is released can be modeled by the function f of t is equal to negative 16 t squared plus v t plus 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?
Answer
A
about 3 seconds
B
about 6 seconds
C
about 1 point 4 5 seconds
D
about 1 point 7 7 seconds
Explanation
Set the height equal to 0 to find when the ball reaches the ground: −16t² + 25t + 6 = 0. The positive solution is t = (25 + √1009) / 32, which is about 1.77 seconds. So the teammate has about 1.77 seconds to catch the ball.
AI-written and checked against the verified answer.