The height of an object thrown upward from the root of a bui

The height of an object thrown upward from the root of a building, 70 feet tall, with an initial velocity of 180 feet/second, is given by the equation h = -16t^2 + 180t + 70 where h represents the height of the object after t seconds. How long will it take the object to reach the ground? (Round answer(s) to nearest tenths place.)

Solution

The height of the object, t seconds after it is thrown up from the roof of a 70 ft. tall building is given by h = -16t² +180 t +70. The object will fall to the ground when h = 0, i.e. when -16t² +180t +70 = 0 or, 6t² -180 t -70 = 0 or, 8t² -90t -35 =0. On using the quadratic formula, we have t = [-(-90)±{(-90)²-4*8*(-35)}]/2*8 = [90±(8100+ 1120)]/16 =( 90±9220)/16 = (90±96.0208)/16 = 186.0208/16 = 11.6263 seconds = 11.6 seconds ( on rounding off to the nearest tenth)

Note:

We have taken the + sign only as time cannot be negative.