Final answer:
The rock takes approximately seconds to reach the ground.
Step-by-step explanation:
The given function h(t) = -4.9t² + 75 represents the height of the rock in meters, t seconds after it is dropped. To find the time it takes for the rock to reach the ground, we need to find when the height is equal to 0.
Setting h(t) = 0, we get -4.9t² + 75 = 0. Solving this quadratic equation, we can use the quadratic formula.
The quadratic formula is t = (-b ± sqrt(b² - 4ac))/(2a), where a = -4.9, b = 0, and c = 75. Using this formula, we can calculate the approximate time it takes for the rock to reach the ground.
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