# algebra

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a cannonaball is fired stright up into the air at a speed of 80 ft/sec from a height of 2ft. A. when will the cannon ball be 98 ft in the air?
B. when will the cannonball hit the ground?

• algebra -

Vi = + 80

g = -32 ft/s^2 (old text, have not seen these units for years)

h = 2 + Vi t - (32/2) t^2
98 = 2 + 80 t - 16 t^2

16 t^2 - 80 t + 96 = 0
t^2 - 5 t + 6 = 0
(t-2)(t-3) = 0
t = 2 or 3 seconds
Two on the way up, three on the way down

When will h = 0 ?
0 = 2 + 80 t - 16 t^2
8 t^2 - 40 t -2 = 0

t = [ 40 +/- sqrt(1600 +64) ]/ 16

t = [ 40 +/- 40.8 ] / 16
negative time was before we pulled the trigger, use + solution
t = 80.8/16 = 5.05 seconds

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