Question

FREE FALL A rock falls from the top of a cliff that is 25.8 meters high. Use the formula ℎ⁡(𝑡)=−
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⁢𝑔⁡𝑡^2+𝑣⁢𝑡+ℎ0. where 𝑔=9.8⁢ 𝑚/𝑠^2

, to write a quadratic function that models the situation. Determine to the nearest tenth of a second the amount of time it takes the rock to strike the ground. Explain your reasoning.

Answer 1

Take initial velocity v = 0 (dropped) and initial height h0 = 25.8 m. With g = 9.8 m/s^2 the model is

h(t) = −(1/2)(9.8)t^2 + 0·t + 25.8 = −4.9 t^2 + 25.8.

The rock strikes the ground when h(t) = 0:
−4.9 t^2 + 25.8 = 0 → t^2 = 25.8/4.9 ≈ 5.2653 → t ≈ √5.2653 ≈ 2.295 s.

Discarding the negative root, the time to the nearest tenth is 2.3 seconds.