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. In addition, the function d(t) = 85t models the horizontal distance d traveled by the ball. If no one catches the ball, how long will it stay in the air?

Question

anonymous · Answer

find the value of t when h=0

anonymous · Answer

Would you happen to know the answer?? I plugged the function into a graphing calculator

anonymous · Answer

Um not really.  Thats why im asking it.  I did it in my head and got -.1.  I will use a calculator now.

anonymous · Answer

1.625 seconds is what I'm thinking actually haha but I'm not 100% sure

anonymous · Answer

if you plug it in and look at the graph you calculate the distance between the zeros of the parabola

anonymous · Answer

the first zero is at (-0.125,0) and the second one is at (1.5,0). The distance between the two would be 1.625. I'm not totally sure because of the fact that time can't be negative so the first zero would technically not be valid :$

anonymous · Answer

True, this is pretty confusing.  I plugged in zero for f(h) but even that is pretty hard to find.

anonymous · Answer

I got it, t=1.5

anonymous · Answer

oh was it just the second zero??

anonymous · Answer

http://www.rpmullen.com/standards/algebra2/unit_1_1/5_3.pdf

anonymous · Answer

^ that actually relates to your question haha

whpalmer4 · Answer

t=1.5 is correct.  1st zero doesn't matter because it occurs at t = -0.125 and is thus out of the domain of the function for this problem.

whpalmer4 · Answer

initial height of ball at t = 0 is 3 ft — right in the strike zone.  Ball is hit at t=0 and impacts the ground at t = 1.5, so 1.5-0=1.5 seconds flight time, and 85(t) = 1.5*85 = 127.5 ft traveled.  Not exactly crushing the ball!