A: In order to find how long the weight was moving, we need to find the time at which the weight hits the ground, meaning its height is 0. We can set the equation h= -16t^2 + 31t + 2 to 0:
0 = -16t^2 + 31t + 2
Solving this quadratic equation, we find that t is approximately 1.94 seconds.
B: To find the weight's maximum height, we need to find the vertex of the parabolic function h= -16t^2 + 31t + 2. The formula for the x-coordinate of the vertex of a quadratic function y= ax^2 + bx + c is x = -b/(2a). In this case, a = -16, b = 31, so the x-coordinate of the vertex is x = -31/(2*-16) = 31/32 = 0.96875 seconds.
Now plug this x value back into the equation to find the max height:
h = -16(0.96875)^2 + 31(0.96875) + 2 ≈ 31.51 feet
C: Since the weight reached a maximum height of approximately 31.51 feet, and did not reach 15 feet, you did not win a prize at the carnival attraction.
A carnival attraction tests your strength by how far in the air you can drive a weight with a hammer. If the weight reaches 15 feet you win a prize! The equation h= - 16t^2+31t+2 gives the height h of the weight t seconds after you hit it.
A: How long was the weight moving?
B: What was the weight's max height?
C: Did you win a prize? How do you know?
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