SOLUTION: a toy rocket is launched from a 144- foot cliff overlooking the ocean with an initial velocity of 128 feet per second the distance or height, s(measured in feet), of the rocket fro

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Question 709069: a toy rocket is launched from a 144- foot cliff overlooking the ocean with an initial velocity of 128 feet per second the distance or height, s(measured in feet), of the rocket from the ground t second after it is launched can be calculated using the model s= 144+128t-16t^2
a) what is the height of the rocket 5 seconds after it is launched?

B) after how many second does the rocket splash in the water?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
s=+144%2B128t-16t%5E2
a) what is the height of the rocket 5 seconds after it is launched?
This is just another way of asking: "What is s when t = 5?" For this we just substitute 5 for t and solve for s:
s=+144%2B128%285%29-16%285%29%5E2
Simplifying...
s=+144%2B128%285%29-16%2825%29
s=+144%2B640-400
s+=+384
So after 5 seconds the height, s, is 384 feet.

B) after how many second does the rocket splash in the water?
Since the water represents a height of 0, this is just another way of asking: "At what time(s) will the height, s, be zero?" For this we will replace the s with 0 and solve for t:
%280%29=+144%2B128t-16t%5E2
This is a quadratic equation (which often has two solutions). So I will start by putting it in standard ax%5E2%2Bbx%2Bc form:
0=+-16t%5E2%2B128t%2B144
Since one side of the equation is already zero we can proceed to the next step. We factor (or use the Quadratic Formula). The GCF is 16. So we can factor out 16 or -16. Since factoring out -16 will leave the t%5E2 with a positive coefficient and since the positive coefficient makes the rest of the factoring easier I'm going to factor out -16:
0=+-16%28t%5E2-8t-9%29
The second factor factors fairly easily (since we thought to factor out the "-" from in front of t%5E2):
0=+-16%28t-9%29%28t%2B1%29
From the Zero Product Property we know that one (or more) of the factors must be zero. So:
-16 = 0 or t-9 = 0 or t+1 = 0
The first equation is a false statement so it has no solutions. The other two, however, have solutions:
t = 9 or t = -1

Since t represents time we will reject the negative answer. (-1 as t means "one second before we launched the rocket..." which makes no sense.) So there is only one realistic answer to the question. The rocket will hit the water 9 seconds after the launch.