Problema Solution
Alexis throws a softball staight up into the air. The ball leaves her hand when it is exactly 5 feet from the ground. The height h of the ball, in feet, can be written as a function of time t, in seconds, as
h=-16t squared+40t+5.
a) What is the maximum height the ball reaches?
b)Alexis catches the ball 5 feet from the ground. How long was the ball in the air?
Answer provided by our tutors
simplify the quadratic by completing the square:
h=-16t^2 + 40t + 5
=-16(t^2 - (40t)/16) + 5
=-16(t^2 - (5t/2)) + 5
=-16(t^2 + 2(-5/2)t + (25/16)t - 25/16) + 5
=-16(t-5/2)^2 + (-16)(-25/16) + 5
=-16(t-5/2)^2 + 30
=-16(t-2.5)^2 + 30
the maximum height will be 30 feet
the amount of time in the air from 5 feet to 5 feet is 2.5 seconds