Question

A rock is thrown straight up from the top of a bridge that is 75 ft high with an initial velocity of 32 ft/s. The height of the object can be modeled by the equation s(t) = -16t^2 + 32t + 75. Determine the time(s) the ball is lower than the bridge in interval notation.

In two or more complete sentences, explain why (-∞, 0) is not included in the solution.

I tried to solve it, but given that the Critical Numbers/Roots are 0 and 2, the solution should be (-∞, 0) ∪ (2, ∞)

Answer 1

Explanation:

When -16t² + 32t + 75 < 75, -16t² + 32t < 0.

=> 16t(2 - t) < 0, t < 0 or t > 2.

However t < 0 is rejected as time cannot be a negative value. Hence the solution in interval notation is (2, ∞).