Word problem Help

Question

Ben threw a rock straight up from a cliff that was 60 ft above water. If the height of the (h) after (t) seconds is given by the equation.

h=-16t^2+68t+60

How long until the rock hits the water.

 

I set the equation equal to zero:

-16t^2+68t+60 =0

 

And then divided by four

-4(4t^2-17t-15)

 

But i'm not sure where to go from here.

Answer 1

Hi Gates:

 

   You are right on, as far as you went.  By setting h=0, you will be looking at the case where the rock is at the level of the water.  You can tell this because at t = 0, h = 60 (the height where the rock starts on the cliff).  So h = 0 must be 60 ft below that point, where the water is.  So, if you can solve the quadratic equation you set up for t, you should get the time to hit the water.

 

   The good thing about standard-form quadratic equations is that there is that big, beautiful 0 on the right, so that, once you factor out the -4, as you did, you can just divide both sides of the equation by it, without changing the equation.  So your problem reduces to solving 4t² -17t - 15 = 0.

 

I found I was able to factor it, by what I have often seen called the "box method."  I got one negative time (which is "unphysical," and can be ignored in this case), and one positive time.  I confirmed the positive time in the equation, so I think it is correct.

 

If you would like to check an answer, just let me know.  Hope this helps!

Answer 2

Do not set the equation to zero. That would give the time taken for the rock to get back to Ben.
The equation should be set to -60. That would give the time needed to pass Ben and hit the water.

 

-16t² + 68t + 60 = -60

-16² + 68t + 120 = 0           add 60 to both sides

4t² - 17t - 30 = 0                 divide both sides by -4

 

This cannot be factored. You must use the Quadratic Formula.