Question

FREE FALL A rock falls from the top of a cliff that is 25.8 meters high. Use the formula ℎ⁡(𝑡)=−1/2

⁢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.
0 seconds ago

Answer 1

The quadratic model (with initial velocity v = 0) is
h(t) = −(1/2)(9.8)t^2 + 0·t + 25.8 = −4.9t^2 + 25.8 (meters).

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

Discard the negative root (time must be ≥ 0). To the nearest tenth, t ≈ 2.3 seconds.