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?

tertre
Dec 30, 2017

#2**+2 **

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

CPhill
Dec 30, 2017