To determine the height of the hill, we can use the kinematic equations of motion. In this case, we'll focus on the vertical motion of the rock.
Let's break down the information given:
- Initial vertical velocity (v₀y) is 0 m/s because the rock is thrown horizontally.
- The time of flight (t) is 5.70 seconds.
- The acceleration due to gravity (g) is approximately 9.8 m/s² (assuming no significant air resistance).
Using the equation for vertical displacement (Δy) in terms of initial velocity, time, and acceleration:
Δy = v₀y * t + (1/2) * g * t²
Since v₀y is 0, the equation simplifies to:
Δy = (1/2) * g * t²
Substituting the values:
Δy = (1/2) * 9.8 m/s² * (5.70 s)²
Calculating the result:
Δy = (1/2) * 9.8 m/s² * 32.49 s² Δy ≈ 158.59 m
Therefore, the height of the hill is approximately 158.59 meters.