Final answer:
To determine the time(s) when the ball is at a height of 150ft, we can substitute h = 150 and solve the quadratic equation -16t^2 + 100t = 150. By using the quadratic formula, we find two possible values for t: t = 3.75 seconds and t = 2.5 seconds.
Step-by-step explanation:
The equation given in the question is h = -16t2 + v0t, where h is the height, t is the time, and v0 is the initial velocity. To determine the time(s) when the ball is at a height of 150ft, we can substitute h = 150 and solve for t.
150 = -16t2 + 100t
Rearranging the equation, we get 16t2 - 100t + 150 = 0. This is a quadratic equation which can be solved using the quadratic formula.
The quadratic formula is t = (-b ± √(b2 - 4ac)) / (2a). In this equation, a = 16, b = -100, and c = 150.
Plugging in these values, we get t = (100 ± √(1002 - 4 * 16 * 150)) / (2 * 16).
Simplifying further, we have t = (100 ± √(10000 - 9600)) / 32.
This simplifies to t = (100 ± √400) / 32.
Taking the square root, we get t = (100 ± 20) / 32.
This gives us two possible values for t: t = (100 + 20) / 32 = 120/32 = 3.75 and t = (100 - 20) / 32 = 80/32 = 2.5.
Therefore, the ball is at a height of 150ft at two times: t = 3.75 seconds and t = 2.5 seconds.