Multipart question

Question

Suppose that a ball is thrown from the top of a 168-foot building.  The function  models the height in feet,  , of the ball  seconds after it is thrown. 

b) If we assume that ground level means  , when does the ball hit the ground?

c) Find the time(s) the ball will be 264 feet above ground.  {You may use fractions or decimals.  Use a comma to separate values, if necessary}

d) The ball will be at its highest point after  seconds.  Find the height of the ball at that time.

Answer 1

h = -16t^2 + 88t + 168 feet high at time t seconds

when is it at 264 feet?? what is its highest height?? when does it hit the ground??

0 = -16^2 +88t +168,

16t^2 -88t -168 = 0

-16(t-2.75)^2 + 531 = 0

=-16(x-7)(x+1.5)

t = 7 and -1.5. It is at 264 feet in 7 seconds

264 = -16t^2 +88t +168

16t^2 -88t + 96 = 0

t = minus 1 1/2 seconds and 4 seconds

it hits ground in 4 seconds

h' = velocity = v = 0 = -32t +88, t = 88/32 =11/4 seconds at max height

max h = -16(11/4)^2 +88(11/4) + 168 = 121 +242 + 168 = 531 feet

maximum height = 531 feet