Calculating Ledge Height from Free Fall Time

Problem Analysis

The problem describes a car falling from a height and provides the time it takes to reach the ground. We are asked to find the initial height of the ledge. This is a classic free fall physics problem where we can use kinematic equations.

Given Information

• Time of fall, \(t = 0.8\) s
• Acceleration due to gravity, \(g = 10\) m/s² (acting downwards)
• Initial velocity, \(v_0 = 0\) m/s (since the car falls off the ledge, implying it starts from rest)

Physics Principles

We use the second equation of motion for constant acceleration:

\(d = v_0 t + \frac{1}{2} a t^2\)

Where:

• \(d\) is the distance traveled (which is the height \(h\) in this case)
• \(v_0\) is the initial velocity
• \(a\) is the acceleration (here, \(g\))
• \(t\) is the time

Calculation Steps

1. Substitute known values into the equation:

   \(h = (0 \text{ m/s}) \times (0.8 \text{ s}) + \frac{1}{2} \times (10 \text{ m/s}^2) \times (0.8 \text{ s})^2\)

2. Simplify the equation: The term \(v_0 t\) becomes zero because \(v_0 = 0\).

   \(h = 0 + \frac{1}{2} \times 10 \text{ m/s}^2 \times (0.8 \text{ s})^2\)

3. Calculate the square of time: \((0.8 \text{ s})^2 = 0.64 \text{ s}^2\).

   \(h = \frac{1}{2} \times 10 \text{ m/s}^2 \times 0.64 \text{ s}^2\)

4. Perform the multiplication:

   \(h = 5 \text{ m/s}^2 \times 0.64 \text{ s}^2\)

   \(h = 3.2 \text{ m}\)

Conclusion

The height of the ledge is calculated to be 3.2 meters. This matches Option 4.