You drop a ball from a height of 1.9m , and it bounces back to a height of 1.3m .

a)What fraction of its initial energy is lost during the bounce?
b)What is the ball's speed just before the bounce?

c)what is the balls speed just after the bounce?

Around 7

To answer these questions, we can use the concept of conservation of mechanical energy.

a) To determine the fraction of initial energy lost during the bounce, we need to calculate the initial energy and the final energy.

The initial energy of the ball is given by its potential energy at a height of 1.9m, which can be calculated using the formula:

Initial energy = mgh

Where:
m = mass of the ball
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = initial height (1.9m)

The final energy of the ball is given by its potential energy at a height of 1.3m, which can be calculated in the same way:

Final energy = mgh

To find the fraction of energy lost, we can divide the change in energy by the initial energy:

Change in energy = Initial energy - Final energy
Fraction of energy lost = (Change in energy) / (Initial energy)

b) To find the ball's speed just before the bounce, we can use the conservation of mechanical energy again. The initial energy of the ball is equal to its kinetic energy just before the bounce. We can calculate the initial kinetic energy using the formula:

Initial kinetic energy = (1/2)mv^2

Where:
m = mass of the ball
v = velocity of the ball
g = acceleration due to gravity (approximately 9.8 m/s^2)

Solving for v, we can find the ball's speed just before the bounce:

v = √(2 * (Initial energy) / m)

Now, we can plug in the values and calculate the answers based on the given information.