algebra help needed

Question

A flower pot is tossed off a balcony it's height (in feet) is given by the formula h(t)=-16t^2+9.4t+90 where t is measured in seconds how long will it take the flower pot to hit the ground? round your answers to three decimal places. _____ seconds

Answer 1

h(t) = -16t^2 + 9.4t + 90= 0 = ground level

divide by 2

8t^2 -4.7t -45 = 0

use the quadratic formula

t=4.7/16+/-(1/16)sqr(4.7^2+32(45))

use a calculator

= (4.7+ sqr1462.09)/16

= 2.683580342

= about 2.684 seconds to hit the ground from 90 feet high

rough check

in 3 seconds it's h=-16(9)+9.4(3)+90

=-144+28.4 +90

=-144+118.4

= -25.6 feet underground

so, t<3

in 2 seconds it's

h=-16(4)+9.4(2)+90

=-64 +18.8+90

= 108.8-64 =44.8 feet in the air

so, 2<t<3

t=2.684 is in the right general range

a few other methods

graph the equation and see where it intersects the x axis

use one of the online equation solvers. they do it all for you including showing the steps needed, mathpapa or symbol lab among other websites

you can't factor the quadratic, but you could complete the square

all the above ignores air resistance, which delays slashdown slightly

Answer 2