SOLUTION: I have a chapter nine test tomarrow 4/26 and i need help! ok..it has to do with quadrtatic equations..Vertical motion models: droped and thrown H=-16t squared + s and -16t

Question 133644This question is from textbook mc dougal fl. algebra 1
: I have a chapter nine test tomarrow 4/26 and i need help!
ok..it has to do with quadrtatic equations..Vertical motion models: droped and thrown H=-16t squared + s and -16t squared+vt+s
the question is.. A falcon dives toward a pigeon on the ground.
when the falcon is at a height if 100 ft the pigeon sees the falcon. which is diving at a 220 ft per sec. estimate the time the pigeon has to escape.

h= height t= time s= initial height v= initial velocity
for some reason you also have to use the quaratic formlua
-b +- squareroot of b squared - 4 (a)(C) over 2(a) This question is from textbook mc dougal fl. algebra 1

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Ok, remember up is positive, down is negative. (it is that convention that causes us to put the negative sign on the lead coefficient in )

Starting at 100 feet ( and starting at a velocity of 220 feet per second downward () with an acceleration downward due to gravity of 16 ft per second per second (), what is the time required for the falcon to reach 0 height (the ground). I use and for initial velocity and distance because that is the value of those quantities at time .

Just substitute the values to produce the following quadratic equation:
)

Just to make the numbers more manageable, divide the whole thing by -4 producing this equivalent quadratic equation:
)

Using the quadratic formula, with , , and we get:

, so

or

A little calculator work shows that is a little less than -14. A negative result for a time measurement doesn't make any sense, so let's exclude this result as an extraneous root.

The calculator says that is a little over 0.44 seconds. The pigeon has a little less than half a second to avoid becoming the falcon's lunch.

Of course, this calculation doesn't tell the whole story. We would have to know how far a very frightened pigeon on the ground can move in 0.44 seconds, and then we would have to know something of the aerodynamics of a diving falcon -- specifically: can the falcon alter his trajectory in that time to compensate for the movement of the escaping pigeon?
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