SOLUTION: If a ball is thrown directly upward with a velocity of 52 feet per second,its height(in feet) after t seconds is given by y=52t-16t^2. what is the maximum height attained by the ba

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: If a ball is thrown directly upward with a velocity of 52 feet per second,its height(in feet) after t seconds is given by y=52t-16t^2. what is the maximum height attained by the ba      Log On


   



Question 638864: If a ball is thrown directly upward with a velocity of 52 feet per second,its height(in feet) after t seconds is given by y=52t-16t^2. what is the maximum height attained by the ball?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Put the equation in the form +y+=+ax%5E2+%2B+b%2Ax+%2B+c+
The x-co-ordinate of the maximum is +x%5Bmax%5D+=+-b%2F%282a%29+
+y+=+-16t%5E2+%2B+52t+
+a+=+-16+
+b+=+52+
+t%5Bmax%5D+=+-52+%2F+%28+2%2A%28-16%29+%29+
+t%5Bmax%5D+=+52%2F32+
+t%5Bmax%5D+=+1.625+ sec
+y+=+-16t%5E2+%2B+52t+
+y%5Bmax%5D+=+-16%2A1.625%5E2+%2B+52%2A1.625+
+y%5Bmax%5D+=+-16%2A2.640625+%2B+84.5+
+y%5Bmax%5D+=+-42.25+%2B+84.5+
+y%5Bmax%5D+=+42.25+
The max height is 42.25 ft
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+5%2C+-5%2C+50%2C+-16x%5E2+%2B+52x+%29+