+0  
 
0
799
3
avatar+311 

The equation $y = -16t^2 - 60t + 54$ describes the height (in feet) of a ball thrown downward at 60 feet per second from a height of 54 feet from the ground, where $t$ represents time, measured in seconds. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest hundredth.

 Mar 26, 2021
 #1
avatar
-3

By the quadratic formula, the ball hits the ground in 0.65 seconds.

 Mar 26, 2021
 #2
avatar+311 
+2

Its actully 0.75. sad

 Mar 26, 2021
 #3
avatar+311 
+4

Setting $y$ to zero, we get the quadratic \[-16t^2 - 60t + 54 = 0.\]Dividing both sides by $-2,$ we get \[8t^2 + 30t - 27 = 0.\]This quadratic factors as $(4t - 3)(2t + 9) = 0.$ As $t$ must be positive, we can see that $t = \frac{3}{4} = \boxed{0.75}.$ laugh

 Mar 26, 2021
edited by WillBillDillPickle  Mar 26, 2021
edited by WillBillDillPickle  Mar 26, 2021

0 Online Users