Question

Ben dives from a 36-foot platform. The equation h=-16t^2+14t+36 models the dive. How long will it take Ben to reach the water?

Answer 1

Let's look at that equation:

\[h(t) = -16t^2+14t+36\]At \(t=0\) he hasn't yet taken his dive:

\[h(0) = -16(0)^2 + 14(0) + 36 = 0 + 0 + 36\]36 feet up, and it's a 36 foot tower.

What will the value of \(h(t)\) be when he reaches the water?

Answer 2

Zero?

Answer 3

Wait would it be 72?

Answer 4

Yes, the water is at 0. If you sketch the graph of that function, it starts out at 36 at t=0 and gets smaller: t=0 is the peak.

So if the water is at height 0, set \(h(t) = 0 = -16t^2 + 14t + 36\] and solve for the value of \(t\) that makes that true.

Answer 5

put h=36 and find the values of t,
\[36=-16t ^{2}+14t+36\]
\[-2t(-8t+7)=0,t=0`gives~the~time~of~starting,-8t+7=0,t=\frac{ 7 }{ 8 }\]

Answer 6

Oh wow thank you guys so much!!!!

Answer 7

yw

Answer 8

No, that's incorrect!

Answer 9

The water is at height h = 0!

Do as I said and solve \[h(t) = 0 = -16t^2+14t +36 \]for the (positive) value of \(t\) where \(h(t) = 0\).

If you think the other approach is correct, then consider this:
At t = 7/8, look at the height of the diver:
\[h(\frac{7}{8}) = -16(\frac{7}8)^2+14(\frac{7}8)+36 = -\frac{49}{4} + 49/4+36 = 36 \]That's not water level, that's the level at which he started!

Answer 10

This is why we check our answers :-)

Answer 11

sorry i am wrong Mr .whpalmer is correct.

i took h from top, actually it is from the ground.
when t=0, h=36
thank you for correcting me.

Answer 12

Here's the path of the diver expressed as height vs. time. Notice that he goes up initially and then down. What @surjithayer found was the time at which the diver returned to his initial height. An equally reasonable thing for a problem to ask, but not what this one did. Whenever I do a word problem like this, I like to reread the problem before I check my answer, just to be certain that I've actually solved the same problem!