A firecracker shoots up from a hill 145 feet high with an initial speed of 80 feet per second. Using the formula H(t) = -16t2 + vt + s, approximately how long will it take the firecracker to hit the ground?

a. 13 seconds b. 11 seconds c. 9 seconds d. 6 seconds

Question

A firecracker shoots up from a hill 145 feet high with an initial speed of 80 feet per second. Using the formula H(t) = -16t2 + vt + s, approximately how long will it take the firecracker to hit the ground?

a. 13 seconds  b. 11 seconds  c. 9 seconds  d. 6 seconds

chaise · Answer

I'm pretty sure you're able to sub in the values:
s=145 (the y intercept of the graph)
and v= 80 (this is how much is changes per a unit)

You get:

H(t) = -16t^2 + 80t + 145

now you just evaluate the function at t=13, 11, 9, 6

H(t) = -16t^2 + 80t + 145 
H(13) = -16*13^2 + 80*13 + 145=
H(11) = -16*11^2 + 80*11 + 145=
H(9) = -16*9^2 + 80*9 + 145=
H(6) = -16*6^2 + 80*6 + 145=

anonymous · Answer

Thank you

chaise · Answer

I think the only time the fire cracker is in the air is when t=6. The rest it has well and truly hit the ground, lol.

although I could be wrong

anonymous · Answer

That is what I came up with

dumbcow · Answer

you could also set H(t) =0 and solve for t using quadratic formula
--> x =6.413
just in case its not multiple choice :)