An arrow is fired

Question

An arrow is fired into the air with an initial velocity of 96 ft./s. The height in feet of the aero T seconds after it was shot into the air is given by the function. H(t)=-16t^2+80t+80. How long after the rocket is launched will it take to strike the ground? Round to the nearest 10th of a second, if necessary.

Answer 1

So to solve this problem, you're going to want to find the value of t at the moment the arrow hits the ground. It hits the ground once the height of the arrow is 0 (in other words it is 0 feet above the ground AKA on the ground). This yields the equation 0 = -16t² + 80t + 80

From here we can divide both sides by 16 to get:

0 = -t² + 5t + 5

and then we can plug this into the quadratic equation to get

t = (-5 ±√(45))/-2

One of these 2 answers is negative, so we can exclude it because it's impossible to have a negative time elapsed, and the other is 5.854 seconds, which we then round to 5.9 seconds.

Hope this helped!