a stone is tossed down from a cliff....

Question

need help!

a stone is tossed down a cliff at an initial velocity of 4ft/sec. the distance S that the stone falls after T seconds is given by S=4T-16T^2 . if the cliff is 420 ft tall, how many seconds will it take for the stone to reach the bottom of the cliff?

Answer 1

Hi Sofia,

 

you have a formula for distance

 

S = 4t -16t²

 

you have a value for the distance you want the stone to travel (420)

 

so put that in the formula and solve for t

 

-420 = 4t - 16t²

 

16t² -4t - 420 =0

 

factor out 4

 

4t² - t - 105 = 0

 

now find the factors for 4t² and -105 that will yield a -1 when combined

 

(4t - 21) (t + 5) =0

 

only one of these will give us a positive answer so we will only solve for that one

 

4t - 21 = 0

 

4t = 21

 

t = 5.25  seconds

 

If you substitute this in the original formula, you will see that it comes up with -420 ft

 

Hope this helps

 

I do have one concern and that is the formula and the words don't agree.  I went with the formula as stated in the problem but if the stone was tossed down, it initial velocity should have been -4t/sec.