SOLUTION: A firework is launched off a building with an initial height of 152 ft, and an initial velocity off 481 ft/s. The firework will explode at 630 ft. How long after setting the firewo

Algebra ->  Rational-functions -> SOLUTION: A firework is launched off a building with an initial height of 152 ft, and an initial velocity off 481 ft/s. The firework will explode at 630 ft. How long after setting the firewo      Log On


   

Question 1100705: A firework is launched off a building with an initial height of 152 ft, and an initial velocity off 481 ft/s. The firework will explode at 630 ft. How long after setting the firework off should the delay be set. Graph.
Found 2 solutions by richwmiller, ikleyn:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
630=-16t^2+481t+152
152-630=478
solve for t
t=1.02898316343029 =1.03
t= 29.0335168365697= 29.03
Unfortunately the graph doesn't show.
I am using a pluggable solver by another tutor
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B481x%2B-478+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28481%29%5E2-4%2A-16%2A-478=200769.

Discriminant d=200769 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-481%2B-sqrt%28+200769+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28481%29%2Bsqrt%28+200769+%29%29%2F2%5C-16+=+1.02898316343029
x%5B2%5D+=+%28-%28481%29-sqrt%28+200769+%29%29%2F2%5C-16+=+29.0335168365697

Quadratic expression -16x%5E2%2B481x%2B-478 can be factored:
-16x%5E2%2B481x%2B-478+=+%28x-1.02898316343029%29%2A%28x-29.0335168365697%29
Again, the answer is: 1.02898316343029, 29.0335168365697. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B481%2Ax%2B-478+%29

Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
.
A firework is launched off a building with an initial height of 152 ft, and an initial velocity off 481 ft/s.
The firework will explode at 630 ft. How long after setting the firework off should the delay be set. Graph.
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The post by @richwmiller is totally  W R O N G.

For your safety,  simply ignore it.

Below please find the correct solution. 

The equation for the height (in feet) as a function of time in seconds is 

h(t) = -16*t^2 + 481*t + 152.


The problem asks to find time moment/moments when h(t) = 630.


The equation takes the form

-16*t^2 + 481*t + 152 = 630  ====>

16*t^2 - 481*t + 630-152 = 0  ====>

16*t^2 - 481*t + 478 = 0


Use the quadratic formula

t%5B1%2C2%5D = %28481+%2B-+sqrt%28481%5E2+-+4%2A16%2A478%29%29%2F%282%2A16%29 = %28481+%2B-+448%29%2F32.


There are TWO solutions:


1)  t%5B1%5D = %28481-448%29%2F32 = 1.03 seconds on the ascending branch, and


2)  t%5B1%5D = %28481%2B448%29%2F32 = 29.03 seconds on the descending branch.






Plot h(t) = -16*t^2 + 481*t + 152 (red) and y = 630 (green)