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Max-Min Problems:

Problem #2:   A ball is thrown straight up, with an initial speed of 64 feet per second, from a cliff 96 feet above the ground.
  1. Where is the ball t seconds later?
  2. When does the ball reach its maximum height?
  3. How high above the ground does the ball rise?
  4. When does the ball hit the ground?
Assume that there is no air resistance and that the accelaration due to the gravity is constant.
 
 
Solution sketch:
  1. s (t) = -16*t2 + 64*t + 96;
  2. Solve for t: s'(t) = -32*t + 64 = 0; Let the solution be t1.
  3. s(t1)is a local maximum. Why is it the maximum height?
  4. Solve for t:
        s(t) = -16*t2+ 64*t + 96 = 0.
    You will find 2 values, but remeber that the solution has to be positive.

 

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Write to: Teresinha Kawasaki