a shell going vertically breaks into 2 equal parts when its speed is 53.9 m/s. one piece rises to afurther height of 122.5m .then the other piece rises to height

To find the height to which the other piece rises, we need to apply the principle of conservation of mechanical energy. This principle states that the total mechanical energy of a system remains constant if there are no external forces acting on it.

The mechanical energy of an object is the sum of its potential energy and kinetic energy. In this case, we can assume that there is no air resistance or any other external force, so mechanical energy is conserved.

Let's break down the solution step by step:

1. Determine the potential energy of the first piece when it breaks into two equal parts at a speed of 53.9 m/s. The potential energy (PE) is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.

2. We know that the first piece rises to a further height of 122.5 m. At this point, the initial kinetic energy of the first piece converts entirely into potential energy. Therefore, we can equate the initial kinetic energy to the potential energy at the new height: (1/2)mv^2 = mgh, where v is the initial speed.

3. Now we can use the information given to solve for the mass of the shell. From step 2, we have (1/2)mv^2 = mgh. We can cancel out the mass m on both sides of the equation, resulting in (1/2)v^2 = gh.

4. Plug in the given values: v = 53.9 m/s and h = 122.5 m.

5. Solve for g by rearranging the equation: g = (1/2)v^2 / h.

6. Calculate g, which is the acceleration due to gravity.

7. Finally, use the equation PE = mgh to find the final height to which the other piece rises. Plug in the calculated gravitational acceleration (g), the known height (h), and the mass (m) of the second piece.

Following these steps, you can find the height to which the other piece rises.