A rubber ball is dropped from height h. It bounces 27" (60%). Write an equation you can use to find height h
.60 h = 27
To find the height from which a rubber ball is dropped given the bounce height, we can use the concept of conservation of energy.
The total energy of the ball at any point can be expressed as the sum of its potential energy (PE) and kinetic energy (KE).
When the ball is dropped, it initially has only potential energy, given by the equation: PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height from which it is dropped.
As the ball bounces, some of its potential energy is converted into kinetic energy and it reaches a certain height which is referred to as the bounce height. At this point, the ball has only potential energy and no kinetic energy.
Using the conservation of energy, we can equate the potential energy at the initial drop height to the potential energy at the bounce height:
PE_initial = PE_bounce
mgh = mg(27)
Here, we use the fact that the bounce height is 60% (or 0.6) of the initial drop height.
Simplifying the equation, we can cancel out the mass (m) and the acceleration due to gravity (g) on both sides:
h = 27/0.6
Therefore, the equation to find the height (h) from which the rubber ball was dropped given the bounce height is:
h = 45 inches