Answer:
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Explanation:
a. To find the maximum height of the rock, we need to find the vertex of the function. The vertex occurs at t = -b/2a, where a = -2.7 and b = 50. So, t = -50 / (2*(-2.7)) = 9.26 seconds. Now we can substitute this value into the equation to find the maximum height:
m = -2.7(9.26)² + 50(9.26) + 6 = 122.2 feet
So the rock will go up to a height of 122.2 feet.
b. To find when the rock will hit the ground, we need to find the time when the height of the rock is 0. So, we can set m = 0 and solve for t:
-2.7t² + 50t + 6 = 0
Using the quadratic formula, we get:
t = (-50 ± sqrt(50² - 4*(-2.7)*6)) / (2*(-2.7))
t = 18.52 seconds or t = 0.21 seconds
Since the negative root doesn't make sense in this context, we can assume that the rock hits the ground after 18.52 seconds.
c. The time it takes for the rock to hit the ground on Earth is given by setting e = 0:
-16t² + 50t + 6 = 0
Using the quadratic formula, we get:
t = (-50 ± sqrt(50² - 4*(-16)*6)) / (2*(-16))
t = 3.71 seconds or t = 0.10 seconds
So, the rock would hit the ground much faster on Earth than on the moon. This is because the gravitational force on the moon is much weaker than on Earth, so it takes longer for objects to fall to the ground.