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

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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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=200769 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.02898316343029, 29.0335168365697. Here's your graph:
Answer by ikleyn(52878)   (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.
~~~~~~~~~~~~~~~~~~~~

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

 =  = .


There are TWO solutions:


1)   =  = 1.03 seconds on the ascending branch, and


2)   =  = 29.03 seconds on the descending branch.






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


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