Can someone help me with this algebra question?

Question

Lauren drove into a swimming pool from a 15-foot-high diving board with an initial upward velocity of 8ft per second. FInd the time 't' in seconds it took Lauren to enter the water. Use the model for vertical motion given by the equation h=-16t^2+vt+s, where 'h' is height in feet, 't' is time in seconds, 'v' is the initial upward velocity in feet per second, and 's' is the initial height in feet. (Hint: Let h=0 represent the surface of the pool.)

Answer 1

OK, so s = 15, v0 = 8, and you're looking for where h = 0:

h(t) = 0 = -16t² + 8t + 15

Divide through by -1 to make it easier:

16t² - 8t - 15 = 0
(4t - 5)(4t + 3) = 0
4t - 5 = 0
t = 5/4 = 1.25 seconds

(The other solution would be t = -0.75 seconds, which you would throw out. If you're curious about why you also get a negative solution, it's equivalent to Lauren jumping from the ground 15 feet to the diving board first.)

Answer 2

Just put all the values in the right place

h=0
v=8
s=15

gives you the following equation

0 = -16 t^2 + 8 t + 15

rearrangin terms you may see

16 t^2 - 8 t - 15 = 0

and dividing by 16

t^2 - 1/2 t - 15/16 = 0

you can solve this for t giving the two roots t = 1.25 s and t = -0.75 s. The last one has no physical meaning because there's no negative times, so yuo just keep t = 1.25 s for the answer.

Answer 3

They basically want you to find the positive x-intercept (or rather t-intercept if you want to be technical) of this quadratic:

-16t^2 + 8t + 15=0 >>> 8 is the initial velocity, and 15 is the height the diver dives from

Basically use the quadratic formula to find the positive solution. (We wouldn't want Lauren to jump back in time eh?)

Answer 4

0 = -16t^2+8t+15
t = 1.25 sec

Answer 5

plug in 0 for h. plug in 8 for v. plug in 15 for s(the original height). then solve for t.

Answer 6

don't expect us dummies to do your home work for you. do you want to be working the graveyard shift at some 7/11 or something?