a 50kg brick bounces with 98% efficiency when droped from a 10 meter ledge.

1.how much energy does it have at the top of the bounce?
2.how high will it bounce?

To answer these questions, we can use the principles of conservation of energy and the concept of elastic collisions.

1. To calculate the energy the brick has at the top of the bounce, we need to determine its initial potential energy (at the top of the ledge) and its final kinetic energy (at the top of the bounce).

The potential energy (PE) at the top of the ledge can be calculated using the formula: PE = mgh, where m is the mass of the brick (50 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the ledge (10 meters). Therefore, the potential energy is: PE = 50 kg x 9.8 m/s² x 10 m = 4900 J.

Since the efficiency is given as 98%, only 2% of the energy is lost during the bounce. Therefore, the brick retains 98% of its initial energy after each bounce.

So, the energy at the top of the bounce is 98% of the initial potential energy, which is: Energy at the top of the bounce = 0.98 x 4900 J = 4802 J.

2. To determine how high the brick will bounce, we can use the principle of conservation of mechanical energy. The total mechanical energy (TE) remains constant throughout the motion, which is the sum of the potential energy (PE) and the kinetic energy (KE) at any point of the motion.

At the top of the bounce, the kinetic energy is zero since the brick momentarily comes to a stop and changes direction. Therefore, the total mechanical energy is solely in the form of potential energy.

Using the conservation of mechanical energy, we can equate the initial potential energy (at the top of the ledge) to the final potential energy at the top of the bounce.

mgh = PE at the top of the bounce

Substituting the given values, we have:
50 kg x 9.8 m/s² x h = 4802 J

Simplifying the equation, we find:
h = 4802 J / (50 kg x 9.8 m/s²)
h = 9.8 meters

Therefore, the brick will bounce to a height of 9.8 meters.