A firecracker shoots up from a hill 155 feet high with an initial speed of 100 feet per second. Using the formula H(t) = -16t2 + vt + s, determine how long it will take the firecracker to hit the ground.

Question

eujc21 · Answer

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phi · Answer

you have an equation that tells you the height of the firecracker.
 $$ H(t) = -16t^2 + vt + s$$
You have s in this formula.  We have to put in a number.  What is the height of the firecracker at t=0 (right before it zooms off)?  sub in 0 wherever you see t in the formula:
H(0)= -16*0*0+v*0+s  which simplifies to 
H(0)= s
so s is the height of the firecracker at the very beginning.  What is its height?
from a hill 155 feet high

I would say 155 ft (the top of the hill).
We also know from the problem that v= initial speed of 100 feet per second.
so the equation is 
$$ H(t)= -16t^2+100t+155 $$

how long it will take the firecracker to hit the ground?
set H(t)=0  (0 is the height when you are on the ground)
$$ 0= -16t^2+100t+155 $$

can you solve a quadratic equation for t?