Question

A boy throws a ball into the air. The equation h = -16t^2 + 28t + 3 models the path of the ball, where h is the height (in feet) of the ball t seconds after it is thrown. How long is the ball in the air? Round your answer to the nearest tenth of a second.

A) About 1.9 sec.
B) About 0.9 sec.
C) About 3.7 sec.
D) About -0.1 sec.

Answer 1

To find the time the ball is in the air, we find the time at which the ball reaches its maximum height. This is achieved when the velocity of the ball is 0. Using the equation for velocity as a function of time, we find that the ball is in the air for approximately 0.9 seconds.

Step-by-step explanation:

The equation h = -16t2 + 28t + 3 models the path of the ball, where h is the height (in feet) of the ball t seconds after it is thrown. To find how long the ball is in the air, we can determine the time at which the ball reaches its maximum height. The maximum height is achieved when the ball stops going up and starts coming back down, which occurs when the velocity of the ball is 0. We can find this time by using the equation for velocity as a function of time: v = -32t + 28. Setting this equation equal to 0, we get -32t + 28 = 0. Solving for t, we find that t = 0.875 seconds. Therefore, the ball is in the air for approximately 0.9 seconds.