Answer :
Final answer:
At the time t=1.8 seconds, the rock is at a height of 86.8 meters and is moving with a velocity of -82.6 m/s.
Explanation:
The question involves a function representing the height of a rock at a given time in seconds: f(t) = -16t² - 25t + 175. To find the height of the rock at the given time t=1.8, we need to substitute t with 1.8 in this equation.
Applying this, the height of the rock f(1.8) = -16(1.8)² - 25(1.8) + 175 = 86.8 meters.
To find out the velocity of the rock at that moment, we need to differentiate the given function because the derivative of a position function gives us the velocity function. The derivative of f(t) = -16t² - 25t + 175 is f'(t) = -32t - 25. Now, substituting t = 1.8 into the velocity function, we get the velocity at t=1.8 as f'(1.8) = -32(1.8) - 25 = -82.6 m/s. Therefore, at the moment t=1.8, the rock is 86.8 meters high and moving with a velocity of -82.6 m/s.
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