SOLUTION: An object is projected vertically upward from the top of a building with an initial velocity of 96 ft/sec. Its distance s(t) in feet above the ground after t seconds is given by th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: An object is projected vertically upward from the top of a building with an initial velocity of 96 ft/sec. Its distance s(t) in feet above the ground after t seconds is given by th      Log On


   

Question 840522: An object is projected vertically upward from the top of a building with an initial velocity of 96 ft/sec. Its distance s(t) in feet above the ground after t seconds is given by the equation
s(t) = −16t2 + 96t + 120.
(a) Find its maximum distance above the ground.
s(t) = ft
(b) Find the height of the building.
Found 2 solutions by josmiceli, amalm06:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the vertex ( or peak ) is
+t%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+96+
+t%5Bmax%5D+=+-96%2F%282%2A%28-16%29%29+
+t%5Bmax%5D+=+3+
Now plug the value of +t%5Bmax%5D+ back
into the equation to find +s%5Bmax%5D+
+s%5Bmax%5D+=+-16%2A3%5E2+%2B+96%2A3+%2B+120+
+s%5Bmax%5D+=+-144+%2B+288+%2B+120+
+s%5Bmax%5D+=+264+
(a)
The max distance above ground is 264 ft
------------------------------------
To find the height of the building, set +t=0+
+s%280%29+=+-16%2A0%5E2+%2B+96%2A0+%2B+120+
+s%280%29+=+120+
(b)
the height of the building is 120 ft
---------------------------------
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+8%2C+-30%2C+300%2C+-16x%5E2+%2B+96x+%2B+120+%29+





Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
The velocity of the object is given by v%28t%29=-32t%2B96

The maximum distance above the ground occurs when the velocity of the ball is 0.

-32t+96=0, therefore t=3. The object reaches its maximum height after 3 s.

a)+s%283%29=%28-16%29%289%29%2B288%2B120=264+ft (Answer)

For b), the ball is at the top of the building at time t=0.

s%280%29=0%2B0%2B120=120+ft (Answer)