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
- Substitute known values into the equation:
\(h = (0 \text{ m/s}) \times (0.8 \text{ s}) + \frac{1}{2} \times (10 \text{ m/s}^2) \times (0.8 \text{ s})^2\)
- Simplify the equation: The term \(v_0 t\) becomes zero because \(v_0 = 0\).
\(h = 0 + \frac{1}{2} \times 10 \text{ m/s}^2 \times (0.8 \text{ s})^2\)
- Calculate the square of time: \((0.8 \text{ s})^2 = 0.64 \text{ s}^2\).
\(h = \frac{1}{2} \times 10 \text{ m/s}^2 \times 0.64 \text{ s}^2\)
- 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.Important Questions from Motion
The rate of change in the velocity of an object per unit time is referred as ________.
Which of the following is a correct equation of motion?
The acceleration of an object is said to be _______ when an object travels in a straight line and its velocity increases or decreases by an equal amounts in equal intervals of time.
What is the friction force employed between the two surfaces interacted in relative speed?
The rate of change of momentum of an object is
