1. ## word problem

Any help would be greatly appreciated because I am totally lost.

A flare is launched upwards at an initial velocity of 80 ft. from a height of 224 ft. Its height, in feet, h(t), after t seconds is given by: h(t)=-16t^2+80t+224
After how long will the flare reach the ground?

Any help would be greatly appreciated because I am totally lost.

A flare is launched upwards at an initial velocity of 80 ft. from a height of 224 ft. Its height, in feet, h(t), after t seconds is given by: h(t)=-16t^2+80t+224
After how long will the flare reach the ground?

Since we want to know when it will hit the ground we are looking for a value of t such that $\displaystyle h(t)=0$ remember h is the height of the flare.

so we need to solve $\displaystyle 0=-16t^2+80t+224$ so if we factor we get..

$\displaystyle 0=-16t^2+80t+224 \iff 0=-16(t^2-5t-14) \iff 0= -16(t+2)(t-7)$ so our two solutions are t=-2 and t=7

We need to disreguard one solution (because it doesn't make sense in the context of the problem) t=-2 so it will take 7 seconds for the flare to hit the ground.

Yeah

3. thank you so much