Question

John throws a ball upward at a rate of 22 meters per second from an

initial height of 3 meters. The height of the ball above the ground can
be approximated by h (t) = -16t2 + 22.0 + 3, where t represents
the amount of time, in seconds, since the ball has been released.
How many seconds will it reach the ground?

Answer 1

1.5 seconds

Explanation:

The height equation is supposed to be ...

h(t) = -16t^2 +22t +3

We want to find the positive value of t where h(t) = 0.

0 = -16t^2 +24t -2t +3 . . . . facilitate factoring

0 = -8t(2t -3) -1(2t -3) . . . . . factor by pairs

0 = -(8t +1)(2t -3) . . . . . . . . complete the factoring

The solutions to this are ...

t = -1/8, 3/2

The ball will reach the ground in 1.5 seconds.