Help with Rate of change question

[Matt2015]

Sorry if this is in the wrong section. I am not sure where to post it.

I am faced with a word problem that I cannot seem to solve, I cant figure it out.

A stunt diver leaps off a bridge 50m above a river with an initial upward velocity of 10m/s. Her altitude is given by h= -5t^2+10t+50, where t is in seconds and h is in metres.

assuming you graph in a table with time versus height you get.
(h,t)= (0,50) (1,55), (2,50) (3,35) (4,10), (5,-25)

The question I am stuck on is finding the time it takes her to hit the water below. I looked online for some help and I cannot follow along with how people come to the answer of 4.31 seconds, I'm hoping I can get a better explanation on these forums. I know you are suppose to solve for T but I don't end up near 4.31. Any help would be greatly appreciated.

 

[ksdhart]

Well, the diver hits the water when her height is zero, so what happens if you set h to zero? You have -5t² + 10t + 50 = 0.

Divide both sides by 5 to get: -t² + 2t + 10 = 0 (0 divided by 5 is still 0). Then solve that with the quadratic formula.

\(\displaystyle t\:=\frac{-2\:\pm \:\:\sqrt{2^2-\left(-40\right)}}{-2}\)

You'll get two answers for t, one of which is roughly -2.31. Since negative time doesn't make sense, you can discard that, leaving only the desired answer of t ~= 4.31 seconds.

 

[stapel]

Sorry if this is in the wrong section. I am not sure where to post it.

What class are you in? Algebra? Calculus? (Not graduate school, so I've moved this out of "Advanced Math".) It generally works well to post to a section that matches what you're studying.

I am faced with a word problem that I cannot seem to solve, I cant figure it out.

A stunt diver leaps off a bridge 50m above a river with an initial upward velocity of 10m/s. Her altitude is given by h= -5t^2+10t+50, where t is in seconds and h is in metres.

assuming you graph in a table with time versus height you get.
(h,t)= (0,50) (1,55), (2,50) (3,35) (4,10), (5,-25)

The question I am stuck on is finding the time it takes her to hit the water below.

What is her height, above water, when she hits the water? Plug that number in for the height, h, and solve for the time, t. Try using one of whatever methods they've taught you for solving quadratic equations, such as the Quadratic Formula.

 

[Matt2015]

I appreciate you moving the thread and I also appreciate the help.

One you mentioned quadratic formula it seemed to click. I guess I am still having issuing realizing when to use what formula.

 

[stapel]

I appreciate you moving the thread and I also appreciate the help.

One you mentioned quadratic formula it seemed to click. I guess I am still having issuing realizing when to use what formula.

Practice, practice, practice is the best way to "get a feel" for what tool to use in which context. In this context, you'll plug the "above water" height of zero (for when she's hitting the water) in for "h", get a quadratic equation, and then... solve the quadratic equation! :wink: