Final answer:
To find the impulse experienced by the stone during its bounce, determine the velocities before and after the bounce using conservation of energy, and then calculate the change in momentum, which is the mass times the change in velocity. The impulse has units of kilogram meters per second.
Step-by-step explanation:
To calculate the magnitude of the impulse I experienced by the stone during the bounce, we first need to determine its velocity just before and just after the bounce. We are ignoring air resistance and using the conservation of energy principle to find these velocities:
- Velocity before the bounce, v1, can be found using the equation K.E. = 0.5 * m * v12 = m * g * h1, where K.E. is the kinetic energy, m is the mass of the stone, g is the acceleration due to gravity (9.8 m/s2), and h1 is the height it was dropped from.
- Velocity after the bounce, v2, is obtained similarly using h2, the height the stone reaches after the bounce.
After calculating v1 and v2, the impulse I can then be calculated using the formula: I = Δp = m * Δ7v, where Δp is the change in momentum, m is the mass, and Δ7v is the change in velocity. Note that the velocities should take direction into account; hence, v2 is positive and v1 is negative (if we assume up is positive).
Once you have the velocities, you can calculate the impulse. Which is the product of the mass and the change in velocity (final velocity after the bounce minus the initial velocity before the bounce). The unit of impulse is kilogram meters per second (kg*m/s).