Answer:
2 seconds
Step-by-step explanation:
The formula h = -16t^2 +vt +s gives the vertical height (in feet) at time t (in seconds) for an object with an initial vertical velocity (in ft/s) of v and an initial height (in ft) of s. The problem statement tells us the ball's initial velocity is v=34 and the initial height is s=4.
Then the equation is ...
h = -16t^2 +34t +4
We want to find the value of t when h=8. There will be two solutions, one when the ball is going up, and the other when the ball is coming down. We are interested in the second solution.
8 = -16t^2 +34t +4
16t^2 -34t +4 = 0 . . . . . subtract the right side of the equation to put it into standard form
(16t -2)(t -2) = 0 . . . . . . factor the equation
Solutions are values of t that make the factors zero:
t = 2/16 or t = 2
It takes 2 seconds for the ball to come down to meet Mike's head.
