MHB Find the average speed of the ball

[coolbeans33]

the height in ft of a baseball, t seconds after being thrown straight upward, is given by h(t)=36t - 16t^2

1) find the average speed of the ball for
a) 0≤ t ≤1
b) .5≤ t ≤ 1
c) .9 ≤ t ≤1

the answer to a) is 20 ft/sec, which is what you get if you plug 1 into the equation. the answer to b) is 12 ft/sec, and c) is 5.6 ft/sec.

how the heck did they get these answers?? I just don't get it. please explain how to do this step by step

also it asks to estimate the speed of the ball after 1 second.

 

[Chris L T521]

Re: find the average speed of the ball

the height in ft of a baseball, t seconds after being thrown straight upward, is given by h(t)=36t - 16t^2

1) find the average speed of the ball for
a) 0≤ t ≤1
b) .5≤ t ≤ 1
c) .9 ≤ t ≤1

the answer to a) is 20 ft/sec, which is what you get if you plug 1 into the equation. the answer to b) is 12 ft/sec, and c) is 5.6 ft/sec.

how the heck did they get these answers?? I just don't get it. please explain how to do this step by step

also it asks to estimate the speed of the ball after 1 second.

The average velocity of a function $h(t)$ over the interval $[a,b]$ (i.e. $a\leq t\leq b$) is given by the formula

\[h_{\text{ave}}=\frac{h(b)-h(a)}{b-a}.\]

Do you think you can do each part knowing this formula now?

I hope this helps!