Understanding Free Fall: Calculating Height and Time from Impact Velocity

The Physics Problem: Determining Fall Parameters of a Pipe Wrench

Question:

A pipe wrench at a construction site strikes the ground with a speed of 24 meters per second. The problems to solve are:

1. From what height was the wrench dropped?
2. How long was the wrench falling?
3. Sketch graphs of position (y), velocity (v), and acceleration versus time for the wrench's fall.

Solution: Analyzing Free Fall Motion

To solve these problems, we apply the principles of free fall:

Phase 1 - Calculating the Drop Height

• The height from which the wrench was dropped can be calculated using the equation: v² = v₀² + 2a(y - y₀), where 'v' is the final velocity (24 m/s), 'a' is the acceleration due to gravity (-9.8 m/s²), and v₀ is the initial velocity (0 m/s for a drop).

Phase 2 - Determining the Fall Time

• The time taken for the fall is found using the equation: v = v₀ + at, substituting the values for 'v', 'a', and v₀.

Phase 3 - Sketching the Graphs

• Position (y) vs. Time: The graph shows a parabolic decrease, starting from the initial height down to 0.
• Velocity (v) vs. Time: This graph is a straight line, starting from 0 and increasing linearly with time.
• Acceleration vs. Time: The acceleration due to gravity is constant, so this graph is a horizontal line at -9.8 m/s².

By applying these principles and calculations, we can find the drop height, fall time, and sketch the required graphs for the wrench's fall.