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Question

A cannon ball is launched into the air with an upward velocity of 324 feet per second, from a 14-foot tall cannon. The height hh of the cannon ball after tt seconds can be found using the equation h=−16t2+324t+14h=-16t2+324t+14.

Approximately how long will it take for the cannon ball to be 1361 feet high? Round answers to the nearest tenth if necessary. units

How long will it take to hit the ground? units

Answer 1

-16t^2 + 324t + 14 = 1361

-16t^2 + 324t = 1361-14 = 1347

-16t^2 +324t -1347

t = 324/32 + or - (1/32)sqr(324^2 -48(1347) = (324+ or - 200.8)/32 = about 3.9 or 16.4 seconds

about 4 seconds and it reaches 1347 ft on the way up, then again at about 16 seconds on the way down

it reaches maximum height at about 10 seconds (324/32)

-16t^2 + 324t + 14

set = 0 and solve for t for when it hits the ground

-8t^2 + 162t + 7 = 0

t = 162/16 + (1/16)sqr(162^2 + 32(7)) = (162+163)/16 = 325/16 = about 20.3 seconds to reach the ground