Question 1076898: hi please i need your help with this problem
an object is projected vertically upward from the ground at an initial velocity of 192 feet per second if air resistance is neglected, its distance s(t) is given by s(t)=-162t^2+192
a-find the maximum height the object reaches and the number of seconds it takes to reach that height. write the answer using a complete sentence
b- when will the object hit the ground
thank you
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! If the object is launched vertically at an initial velocity of 192 ft./sec, then the equation describing it's motion would be -16tē+192t, where t is time, in seconds, after launch.
a)The time needed to reach maximum altitude is given by the expression -b/2a, for an equation of the form atē+bt+c. In this case we get the value of:
-b/2a=-192/-32=6
After 6 seconds our object is at a height of h=-16(6ē)+192(6), or 576 ft.
b)When the object hits the ground, its' height is 0, so:
0=-16tē+192t
16tē=192t
16t=192
t=12
The object hits the ground after 12 seconds. ☺☺☺☺
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