Final answer:
To determine the height from which an object is dropped, one can use the equation v = √(2gh), where g is the acceleration due to gravity (9.8 m/s²) and h is the height in meters. An experiment can be conducted by dropping the object and timing its fall to calculate the velocity upon impact and verify the initial height. Multiple trials can improve the accuracy of these measurements.
Step-by-step explanation:
How to Determine the Height of a Dropped Object
When an object is dropped, calculating its final velocity and the height it was dropped from can be achieved using kinematic equations. Based on the assumption that the object is dropped from rest, and the bounce is negligible, we can use the following equation to determine the velocity of the object when it hits the ground:
Velocity (v) = √(2 * acceleration due to gravity (g) * height (h))
The acceleration due to gravity is a constant 9.8 m/s². If we know the height from which the object was dropped (like a phone from chest height), we can insert this value into our equation to calculate the velocity upon impact. Additionally, to estimate the object's potential and kinetic energy, you can use the formula:
PE = KE
, where PE is potential energy and KE is kinetic energy.
To determine the exact velocity, you can carry out an experiment where one partner drops the object while another partner times the fall. With the time (t) recorded, use the formula:
Velocity (v) = acceleration due to gravity (g) * time (t)
By averaging multiple measurements, you can obtain an accurate value for the velocity. To verify your calculations, you can compare the experimental results with predicted values based on kinematic formulas.
Designing an Experiment to Measure Height and Velocity
For a more comprehensive understanding, students could design an experiment involving a two-dimensional ballistic motion. This would involve measuring the time of flight and comparing it to the maximum height reached by an object. Variations in height and initial velocities can be explored to demonstrate how they affect the object's time of flight and impact velocity.