Question

A ball is thrown straight up from the top of a building that is 185ft high with an initial velocity of 64ft/s. The height of the object can be modeled by the equation s(t) = -16t 2 + 64t + 185.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.

Answer 1

To find the interval in which the ball is higher than the building, solve the inequality h(t) > 185. The inequality is easily solved by subtracting 185 so the comparison is to zero, factoring the expression involving t, and identifying the time interval in which the signs of the factors are the same.

  -16t² +64t +185 > 185
  -16t² +64t > 0
  (-16t)(t -4) > 0
Both factors will have negative signs on the interval (0, 4).