How High Does a Basketball Bounce After Losing 20% Energy?

[aleferesco]

Homework Statement

A basketball is dropped from a height of 2m. It lost lost 20% of its energy, in the bouncing from the floor due to friction in the air, before it reaches the highest point of its first bouncing. How high did it bounce?

h1= 2m
h2=?
g=9.8m/s^2

Homework Equations

PE = mgh and Energy Total (initial)=Energy Total (final)

mgh1 = 0.20 + mgh2

The Attempt at a Solution

I don't know how to solve it without the mass and kinetic energy

 

[PhanthomJay]

Homework Statement

A basketball is dropped from a height of 2m. It lost lost 20% of its energy, in the bouncing from the floor due to friction in the air, before it reaches the highest point of its first bouncing. How high did it bounce?

h1= 2m
h2=?
g=9.8m/s^2

Homework Equations

PE = mgh and Energy Total (initial)=Energy Total (final)

mgh1 = 0.20(?) + mgh2

check this equation for an error...20% of what?

The Attempt at a Solution

I don't know how to solve it without the mass and kinetic energy

What's the initial KE at the release point? What's the final KE at the top of the first bounce?

 

[baba89]

.

I would approach this problem by first acknowledging that the given information is incomplete and that we would need to make certain assumptions in order to solve it. One possible assumption we could make is that the basketball has a constant mass throughout the process, and that the loss of energy due to friction is negligible compared to the potential energy of the basketball.

With this assumption, we can use the conservation of energy principle to solve for the height of the bounce. The initial energy of the basketball is its potential energy at a height of 2m, which is given by mgh1. The final energy of the basketball is the sum of its remaining potential energy after the bounce, which is mgh2, and the energy lost due to friction, which is 20% of the initial potential energy (0.20mgh1).

Setting these two energies equal and solving for h2, we get:

mgh1 = 0.20mgh1 + mgh2

h2 = h1 - 0.20h1

h2 = 2m - 0.20(2m)

h2 = 1.6m

Therefore, the basketball bounces to a height of 1.6m after the first bounce. However, it is important to note that this solution is based on certain assumptions and may not be entirely accurate. In order to get a more precise answer, we would need more information such as the mass of the basketball and the exact amount of energy lost due to friction.