Question

Word problem! Help me?
A baseball is thrown upward into the air at a velocity of 30ft/s. Its height h, in feet, after t seconds is given by the function h=-16t^2+30t+6
How long will it take the ball to reach its maximum height?
What is the balls maximum height?
What is the range of the function?

Answer 1

Like this right?
h
= -16t^2 + 30t + 6
= (-16t^2 + 30t) + 6
= -16(t^2 - (15/8)t) + 6
= -16(t - (15/16))^2 + 16(15/16)^2 + 6
= -16(t - (15/16))^2 + (321/16)
So, then what's the range of the function?

Answer 2

Well, \(\frac{d}{dt}(-16t^2+30t+6) = -32t+30\), so, setting that equal to zero and solving for t gives, \(-32t+30 = 0 \rightarrow 30 = 32t \rightarrow t = \frac{30}{32} = \frac{15}{16} = t\). So at \(t=\frac{15}{16}s\), the ball is at its maximum height. :)

Answer 3

My guess for the range is, plug in zero for t in the original function and find out the height. Now you know your range will be between that minimum height when t=0, and the maximum height, that you find when \(t=\frac{15}{16}\).

Answer 4

I.e., the minimum height is 6, because the person who threw it released the ball at 6 feet high.