A baseball player hits a ball toward the outfield. The height h of the ball in feet is modeled by h(t) = -16t2 + 22t + 3, where t is the time in seconds. If no one catches the ball, how long will it stay in the air? (Round to the nearest tenth of a second and enter only the number.)
HINTS:
• When the ball hits the ground, its height is zero, so you are looking for one of the zeros of the quadratic equation.
• Though you could use several different methods, the easiest way to solve this particular equation is the quadratic formula (provided here). Take the a, b, and c values from the function in the question above.
• When you solve the quadratic for the zeros, you will have two answers. One of the answers will not make sense for a baseball hit into the outfield. The one that does make sense will be the correct answer.
Answer (3)
Solving this equation for the roots, we find that the roots are -1/8 and 3/2. Assuming that at t=0 is when the player hits the ball, t=0 and t=3/2 is the amount of time in the air. Therefore, the ball spent 3/2 seconds in the air, or 1.5 seconds.
The time that the baseball stays in the air is determined by setting h(t), the height, to 0 and solving for t (time) using the quadratic formula; the positive answer represents the time in seconds that the ball stays in the air. ;
The baseball stays in the air for approximately 1.5 seconds, as determined by solving the quadratic equation for the height of the ball and finding the positive solution for time. We set the height equation equal to zero and applied the quadratic formula. The only meaningful solution for time is positive, leading to 1.5 seconds.
;
