Final answer:
By setting the quadratic equation h(t) representing Sara's height above the water to zero and factoring it, we find that Sara takes 3 seconds to hit the water. Therefore, the correct option is b).
Step-by-step explanation:
The problem presented is a quadratic equation representing the motion of a diver in terms of her height above the water at any given time. To determine how many seconds it takes for Sara to reach the water, we need to find when her height above the water, h(t), equals zero. The equation given is h(t)=-5t^2+10t+15, which is a parabolic equation that will intersect the t-axis (time) at the point where Sara hits the water.
To find when Sara reaches the water, we set h(t) to 0 and solve for t:
0 = -5t^2 + 10t + 15.
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. However, for the sake of this exercise, we will attempt to factor first:
-5t^2 + 10t + 15 = 0
Dividing through by -5 to simplify:
t^2 - 2t - 3 = 0
Factoring the quadratic:
(t - 3)(t + 1) = 0
Setting each factor equal to zero gives us two potential times when Sara's height is 0:
t = 3 or t = -1.
Since a negative time does not make sense in this context, we discard t = -1. Therefore, the time it takes for Sara to reach the water is 3 seconds.
The correct option is (b) 3 seconds. This can be determined without the quadratic formula, as the equation was factorable. It’s important to interpret the result within the context of the problem, disregarding non-sensical answers such as negative time.