SOLUTION: Really need your help! Height of a ball: If a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y = 40t - 16t^2. What is

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Really need your help! Height of a ball: If a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y = 40t - 16t^2. What is       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 904102: Really need your help!
Height of a ball: If a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y = 40t - 16t^2. What is the maximum height attained by the ball?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
25 ft after 1.2 seconds
-32t+40=0
t=40/32=5/4
40t - 16t^2
40*5/4 - 16*25/16
y=50-25=25 ft







Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The given formula is a parabola with a vertex
that is a maximum. Here's a plot:
+graph%28+400%2C+400%2C+-1%2C+4%2C+-10%2C+30%2C+-16x%5E2+%2B+40x+%29+
--------------------
When the parabola has the form:
+a%2Ax%5E2+%2B++b%2Ax+%2B+c+, the x-coordinate of
the maximum is at:
+-b%2F%28+2a+%29+
+a+=+-16+
+b+=+40+
+-b%2F%282a%29+=+-40%2F%282%2A%28-16%29+%29+
+-b%2F%282a%29+=+40%2F32+
+40%2F32+=+5%2F4+
At +t+=+5%2F4+, the height is a maximum
+y%5Bmax%5D+=+-16t%5E2+%2B+40t+
+y%5Bmax%5D+=+-16%2A%285%2F4%29%5E2+%2B+40%2A%285%2F4%29+
+y%5Bmax%5D+=+-16%2A%2825%2F16%29+%2B+50+
+y%5Bmax+%5D+=+50+-+25+
+y%5Bmax%5D+=+25+ ft
This matches the plot