Question

During a high school baseball tournament, Lexile hits a pitch and the baseball stays in the air for 4.42 seconds. The function describes the height over time, where h is its height, in yards, and t is the time, in seconds, from the instant the ball is hit: h(t) = - 5t ^ 2 + 22t + .5

Answer 1

Answer:

a) The maximum height that the ball reaches is 73.1 meter

b ) The time elapsed when the ball reaches its maximum height of flight = 2.2 seconds

Step-by-step explanation:

The complete question is

During a high school baseball tournament, Lando hits a pitch and the baseball stays in the air for 4.42 seconds. The function h(t) = -5t2 + 22t + 0.5 describes the height over time, where h is its height, in meters, and t is the time, in seconds, from the instant the ball is hit. a. What is the maximum height the ball reaches? b. What will be the time elapsed when the ball reaches its maximum height of flight?

Solution:

For maximum height

$\frac{dh}{dt} =0$

$\frac{d(5t^2 + 22t + 0.5)}{dt}\\ 10t + 22 = 0\\t = 2.2$seconds

a) Maximum height

$5 * t^2 + 22t + 0.5$

$= 5 * 2.2 *2.2 + 22 * 2.2 + 0.5 \\= 73.1$

b) Time elapsed when the ball reaches maximum height is 2.2 seconds