# Falling object

• Jul 11th 2007, 09:43 PM
lilmama-14
Falling object
At time=0, a diver jumps from a diving board that is 32 feet above the water. the hieght of the diver is given by the equation,
h(t)=-16t (squared) +16t+32, where h is measured in feet and t is measured in seconds.

A)when does the diver hit the water?

B)what is the domain of the equation for height?

C)what is the range of the equation for the hieght?

D)what is the maximum height reached by the diver?
• Jul 11th 2007, 10:00 PM
Jhevon
This has nothing to do with geometry

[quote=lilmama-14;60314]At time=0, a diver jumps from a diving board that is 32 feet above the water. the hieght of the diver is given by the equation,
h(t)=-16t (squared) +16t+32, where h is measured in feet and t is measured in seconds.

A)when does the diver hit the water?
[\quote]
he hits the water when his height above the water is zero.

solve for h(t) = 0

that is, $-16t^2 + 16t + 32 = 0$

Quote:

B)what is the domain of the equation for height?
the domain of a function is the set of all inputs (in this case, t-values) for which the function is defined. technically, the domain of this function is all real t, since it is a polynomial. but generally we don't accept negative values for time, so i'd say dom(h) = $[0, \infty)$

Quote:

C)what is the range of the equation for the hieght?

the range is the set of all outputs (in this case, h-values) for which the function is defined. the function given is a parabola with a maximum value. find this maximum value. the range will be everything from that value down to -infinity

Quote:

D)what is the maximum height reached by the diver?
i'm tempted to just blurt out 32 , since the diver was at 32 feet and is diving downwards(but that is likely to be wrong, since it's possible his height increased before it started to decrease), but let's be methodical about this.

the maximum height occurs at the vertex. to find the t that gives the vertex, we use the vertex formula: $t = \frac {-b}{2a}$, where the original equation is of the form: $h = at^2 + bt + c$

after finding the t-value in this way, plug it into h to solve for the max height
• Jul 12th 2007, 05:43 AM
topsquark
I believe Jhevon gave an incorrect answer for B) and also gave an incorrect answer for C) due to the same flaw.

The equation $h(t) = -16t^2 + 16t + 32$ is valid only for the diver's height for the time period that the diver is in the air. So it is true only from t = 0 s to t = 2s (when the diver hits the water.) So the domain of the function is [0, 2].

As to the range of the function, again the function is only defined for when the diver is in the air. So the range will include only 0 ft (the surface of the water) to whatever the maximum height is.

-Dan
• Jul 12th 2007, 09:22 AM
Jhevon
Quote:

Originally Posted by topsquark
I believe Jhevon gave an incorrect answer for B) and also gave an incorrect answer for C) due to the same flaw.

The equation $h(t) = -16t^2 + 16t + 32$ is valid only for the diver's height for the time period that the diver is in the air. So it is true only from t = 0 s to t = 2s (when the diver hits the water.) So the domain of the function is [0, 2].

As to the range of the function, again the function is only defined for when the diver is in the air. So the range will include only 0 ft (the surface of the water) to whatever the maximum height is.

-Dan

yes, i did err. i mentioned that the domain and range were values for "which the function was defined." but obviously infinity would not come into play, or the guy would be diving forever! The function is only defined for the period the diver is in the air, duh! ...why did i write otherwise:confused:

Thanks Dan! I'd give you two thanks for your post if i could!
• Jul 12th 2007, 11:07 AM
topsquark
Quote:

Originally Posted by Jhevon
yes, i did err. i mentioned that the domain and range were values for "which the function was defined." but obviously infinity would not come into play, or the guy would be diving forever! The function is only defined for the period the diver is in the air, duh! ...why did i write otherwise:confused:

Thanks Dan! I'd give you two thanks for your post if i could!

No worries. It happens to the best of us. Well, not me, but the best of everyone else. (I'm soooo humble. :p )

-Dan
• Jul 12th 2007, 12:45 PM
ThePerfectHacker
Quote:

Originally Posted by topsquark
(I'm soooo humble. :p )

You learned that from me. :cool:
• Jul 12th 2007, 12:52 PM
topsquark
Quote:

Originally Posted by ThePerfectHacker
You learned that from me. :cool:

Trust me, I was proud of my humility long before you were born! :rolleyes:

-Dan