SOLUTION: The height s, in feet, of a rock thrown upward at an initial speed of 64 ft/sec from a cliff 50 ft above an ocean beach is given by the function s(t)=-16t^2+64t+50, where t is the

Algebra ->  Functions -> SOLUTION: The height s, in feet, of a rock thrown upward at an initial speed of 64 ft/sec from a cliff 50 ft above an ocean beach is given by the function s(t)=-16t^2+64t+50, where t is the      Log On


   



Question 745110: The height s, in feet, of a rock thrown upward at an initial speed of 64 ft/sec from a cliff 50 ft above an ocean beach is given by the function s(t)=-16t^2+64t+50, where t is the time in seconds. Find the maximum height above the beach that the rock will attain.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum height of this parabolic curve is
+s%5Bmax%5D+ when +t+=+-b%2F%282a%29+ and
the equation has the form:
+s%28t%29+=+at%5E2+%2B+b%2At+%2B+c+
In your equation,
+s%28t%29+=+-16t%5E2+%2B+64t+%2B+50+
+a+=+-16+
+b+=+64+, so
+t+=+-64+%2F+%28+2%2A%28-16%29%29+
+t+=+-64+%2F+-32+
+t+=+2+ sec
--------------
Now find +s%282%29+ which is the maximum height
+s%282%29+=+-16%2A2%5E2+%2B+64%2A2+%2B+50+
+s%282%29+=+-64+%2B+128+%2B+50+
+s%282%29+=+114+ ft
The maximum height is 114 ft
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+5%2C+-10%2C+130%2C+-16x%5E2+%2B+64x+%2B+50+%29+