Solve Quadratic Equations by Quadratic Formula

Question

The height in feet h of an object shot upwards in to the air with initial velocity v0 after t seconds is given by the formula h(t) = −16t^2 + (v0)t

A firework is shot upwards with an initial velocity of 110 feet per second. How many seconds will it take to reach a height of 171 feet? Round your answer to the nearest tenth of a second.

Answer 1

171 = -16t^2 + 110t

16t^2 -110t + 171 = 0

t = 110/32 + or - (1/32)sqr(110^2 -4(16)(171))

t = (110 + or - 34)/32 = 144/32 or 76/32 = 2.375 or 4.5 seconds to reach 171 feet

you want the nearest tenth, so t = 2.4 or 4.5

it reaches that height once on the way up, then again on the way back

it reaches maximum height at the mid time (2.375 + 4.5)/2 = 3.4375 seconds