A person standing close to the edge on the top of a 160-foot building throws a baseball vertically upward. the quadratic function
s(t) = -16t^2+64t+160
models the ball's height above the ground, s(t), in feet, t seconds after it was thrown
a) after how many seconds does the ball reach its maximum height? What is the maximum height?
b) How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second
so I have found a) as 2 seconds and 224 feet but how do i figure out part b?

Question

A person standing close to the edge on the top of a 160-foot building throws a baseball vertically upward.  the quadratic function 
s(t) = -16t^2+64t+160
models the ball's height above the ground, s(t), in feet, t seconds after it was thrown 
a) after how many seconds does the ball reach its maximum height? What is the maximum height?
b) How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second
so I have found a) as 2 seconds and 224 feet but how do i figure out part b?

jim766 · Answer

axis of symetry     -b/2a    -64/-32  = 2
        x = 2 is a vertical line that goes through the max
        in this case x = 2 seconds when it reaches max height

questions?

anonymous · Answer

I got that part I just need for part b saying how many seconds does it take until the ball finally hits the ground ... round to the nearest 10th

jim766 · Answer

you can use two methods, you could graph it on a graphing calculator and see what x =, when the graph crosses the x axis.

Doing it by hand,  
When the rock hits the ground the height will be zero, so set the equation equal to zero.

0 = -16t^2+64t+160    now factor it
0 = -16(t^2 - 4t -10)    
 you would then use the quadratic formula
to factor t^2-4t-10
          
Honestly, it is much easier to use the calculator and graph it if you can.