The time between the rock’s drop and landing is t = 1.8 s
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In the given equation: h(t) = 25t^2 - 81, it is dropped from a height, h, and the variable, t, represents the total time. We want to solve for t.
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The height when the rock lands will be 0 m.
Plug 0 into the equation for h and
(0)t = 25t^2 - 81
0 = 25t^2 - 81
81 = 25t^2
Divide both sides by 25 to isolate the variable, t;
81/25 = t^2
Take the square root from both sides to cancel out the exponent;
√(81/25) = √(t^2)
Note that 81 has a sqrt of 9 and 25 has a sqrt of 5. We can also ignore the negative from the ± since time is positive.
9/5 = t
t = 1.8 s