Final answer:
The quadratic equation -16t^2 + 29t - 12 = 0 is solved using the quadratic formula, giving two values t = 3.79 s and t = 0.54 s, when the ball reaches 17 meters in height. However, these results do not align with the potential answers (t = 1, t = -1, t = 2, t = -2) given in the question.
Step-by-step explanation:
To find the values of t for which the ball's height is 17 meters using the formula h = 5 + 29t - 16t2, we must replace 'h' with 17 and solve the resulting quadratic equation:
17 = 5 + 29t - 16t2
12 = 29t - 16t2
0 = -16t2 + 29t - 12
The quadratic equation can be solved using the quadratic formula: t = [-b ± √(b2 - 4ac)] / (2a).
In this equation, a = -16, b = 29, and c = -12. Substituting these values into the quadratic formula:
t = [(-29) ± √(292 - 4(-16)(-12))] / (2(-16))
Solving this will give us the values of 't', which are t = 3.79 s and t = 0.54 s. These represent the times when the ball is at 17 meters, once on its way up and then on its way down. However, none of these time values match the potential answers provided, which suggests there may be an error in the question or that it's a trick question.