Question

When a baseball is hit by a batter, the height of the ball, h(t), at time t, mc018-1.jpg, is determined by the equation mc018-2.jpg. If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?
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Answer 1

I can't see the images you attached. Please either type the formula for h(t) (or paste the text from the images) or tell me the four answer choices shown.

If you want the general method so you can do it yourself:

1. Write the inequality h(t) ≥ 52.
2. Move 52 to the left: f(t) = h(t) − 52 ≥ 0. This is a quadratic f(t) = at^2 + bt + c.
3. Solve f(t) = 0 with the quadratic formula:
t = [−b ± sqrt(b^2 − 4ac)] / (2a).
4. If a < 0 (parabola opens downward, usual for projectile motion), then f(t) ≥ 0 for t between the two real roots t1 and t2 (with t1 < t2). So the time interval is [t1, t2], but restrict to t ≥ 0 physically.
5. If the discriminant b^2 − 4ac < 0 there are no real roots; then either f(t) is always positive (ball always ≥ 52) or always negative (never ≥ 52) depending on the sign of a.

If you paste the specific h(t) I will solve it and give the numerical time interval.