The feather and the ball both experience a gravitational force towards the centre of the earth which scales in proportion to their mass (the force is greater on the ball than on the feather).
The force manifests itself as an acceleration which scales in inverse proportion to the mass (the same force would make the feather accelerate faster than the ball).
So the proportionalities cancel:
in tabular form-
relative mass for same force for same gravitating body
Feather : low : easy acceleration : low coupling to gravity
Ball : high : sluggish acceleration : higher coupling to gravity
in algebraic form -
acceleration = force/mass = (const. x mass) / mass
if the acceleration is the same, so will the kinematics and they will "fall at the same rate".
Note that there are actually two kinds of mass in this - inertial (that resists acceleration) and gravitational (that couples to a gravitational field). The fact that these are the same is "deep" and leads to Einstein's Genral Theory of Relativity.
The higher the height the ball is dropped from, the higher the height it will bounce to.
Yes - the greater the height an item dropped the resulting bounce is higher
Gravity, air resistance, the material of the ball, and the height from which it was dropped initially.
yes
Yes, assuming the ball has elasticity and you haven't exceeded the height where the ball, when dropped, reaches terminal velocity.
Both will fall at the same time in vacuum because there is no resistance.
The higher the height the ball is dropped from, the higher the height it will bounce to.
Yes - the greater the height an item dropped the resulting bounce is higher
Yes - the greater the height an item dropped the resulting bounce is higher
Yes - the greater the height an item dropped the resulting bounce is higher
Yes.
Gravity, air resistance, the material of the ball, and the height from which it was dropped initially.
Assuming both were dropped from the same height above ground, in a vacuum both would hit the ground at the same time. In a significant atmosphere (e.g. average ground-level on Earch) the bowling ball would hit the ground first.
yes
It all depends on the height the ball has been dropped and the weight of the ball.
Yes, assuming the ball has elasticity and you haven't exceeded the height where the ball, when dropped, reaches terminal velocity.
Increasing the height from which it is released increases the height to which it rebounds.