SOLUTION: The word problem: The height, h, in feet of an object above the ground is given by h(t)=-16t^2 + 64t + 190 where t is the time in seconds. Find the time it takes the object to str
Question 771131: The word problem: The height, h, in feet of an object above the ground is given by h(t)=-16t^2 + 64t + 190 where t is the time in seconds. Find the time it takes the object to strike the ground and find the maximum height of the object.
I have no idea what to do with this equation. I have tried putting h in terms of t and solving from there, but it equals zero. I do not know what else to do. Thanks so much. Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! h, in feet of an object above the ground is given by h(t)=-16t^2 + 64t + 190 where t is the time in seconds. Find the time it takes the object to strike the ground and find the maximum height of the object.
I have no idea what to do with this equation. I have tried putting h in terms of t and solving from there, but it equals zero. I do not know what else to do. Thanks so much.
h(t)=-16t^2 + 64t + 190
at two times the height of the object = 0 when it starts and when it reaches the ground since this a parabola
plug h=0
-16t^2 + 64t + 190 =0
Find the roots of the equation by quadratic formula
a= -16 b= 64 c= 190
b^2-4ac= 4096 - -12160
b^2-4ac= 16256 = 127.5
x1=( -64 + 127.5 )/ -32
x1= -1.98
x2=( -64 -127.5 ) / -32
x2= 5.98
Ignore negative value mph
x = 5.98
time taken = 5.98 seconds
The maximum must occur at the vertex. So let’s find the vertex. We use the formula t =-b/2a (-64)/2*-16= 2 So we have t = 2 seconds.
So at 2 seconds the object reaches its maximum height. we must find the value of the vertex, Find the value of h when t = 2.
We plug this in to the equation -16*(2)^2 + 64*2 + 190 = = 254 feet.
So the maximum height is 254 feet.
