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rebeccacopley8307
05.02.2020 •
Mathematics
Afirecracker shoots up from a hill 160 feet high, with an initial speed of 90 feet per second. using the formula h(t) = −16t2 + vt + s, approximately how long will it take the firecracker to hit the ground?
a. five seconds
b. six seconds
c.seven seconds
d.eight seconds
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Ответ:
H(t) = -16t² + vt + s
Where -16 is half of the gravitational constant of almost 32 ft/sec (downward, thus negative),
v is the initial velocity (90), and
s is the starting height (160)
so we have:
H(t) = -16t² + 90t + 160
How long before it hits the ground? Solve for h(t) = 0:
0 = -16t² + 90t + 160
Divide both sides by -2:
0 = 8t² - 45t - 80
Quadratic equation:
t = [ -b ± √(b² - 4ac)] / (2a)
t = [ -(-45) ± √((-45)² - 4(8)(-80))] / (2(8))
t = [ 45 ± √(2025 + 2560)] / 16
t = [ 45 ± √(4585)] / 16
throwing out the negative time:
t = (45 + √4585) / 16
t ≈ 7.04 seconds
Ответ:
this is 5 points but i'll take the points next time don't say you'll give 100 points just to get a answer
Step-by-step explanation: