+4622 The equation \(y = -4.9t^2 + 42t + 18.9\) describes the height (in meters) of a ball tossed up in the air at 42 meters per second from a height of 18.9 meters from the ground, as a function of time in seconds. In how many seconds will the ball hit the ground?
+129899 When it hits the ground, y will = 0
So we have
-4.9t^2 + 42t + 18.9 = 0 multiply through by -10
49t^2 - 420t - 189 = 0 divide through by 7
7t^2 - 60t - 27 = 0 factor
(7t + 3 ) ( t - 9 ) = 0
Setting each factor to 0 and solving for t gives
t = - 3/7 sec { reject }
And
t = 9 sec
