Final answer:
To find the velocity of the flare at 131 feet, calculate the derivative of the position function to get the velocity function and then solve for the time when the flare is at 131 feet before substituting it back into the velocity function.
Step-by-step explanation:
To find the velocity of the flare when it is at a height of 131 feet and moving toward the ground, we first need to understand that velocity is the derivative of the position function with respect to time (s'(t)). Given the position function s(t) = -3t² + 100t + 3, we can calculate the velocity function:
v(t) = s'(t) = d(-3t² + 100t + 3)/dt = -6t + 100
Next, we set the position function equal to 131 feet and solve for t to find the time(s) when the flare is at that height:
-3t² + 100t + 3 = 131
When we solve this quadratic equation, we find two values of t (time in seconds). One for the ascent and one for the descent. We are interested in the descent part, which is the larger value of t. After finding the appropriate value of t, we plug it into the velocity function to find the velocity at that specific time.