Calculate u in both cases...then sub. in formula 1/2mu^2...fr both cases n take the ration

Analysis of Kinetic Energy of Bodies A and B
Body A is projected vertically upwards while body B is projected at an angle of 60 degrees with the horizontal. Both bodies reach the same height. Let's analyze the ratio of the initial kinetic energy of body A to that of body B.

Initial Kinetic Energy of Body A
- When body A is projected vertically upwards, all its initial kinetic energy is converted into potential energy at the highest point of its trajectory.
- The formula for kinetic energy is KE = 0.5 * m * v^2, where m is the mass of the body and v is the velocity.
- At the highest point, the velocity of body A is zero, so all the initial kinetic energy is converted into potential energy.

Initial Kinetic Energy of Body B
- Body B is projected at an angle of 60 degrees with the horizontal, which means it has both horizontal and vertical components of velocity.
- The initial kinetic energy of body B is divided into two parts: one for the horizontal component and the other for the vertical component.
- The vertical component of velocity at the highest point is zero, so the kinetic energy associated with that component is converted into potential energy.
- However, the horizontal component of velocity remains constant, so the kinetic energy associated with that component is still present.

Ratio of Initial Kinetic Energies
- The ratio of the initial kinetic energy of body A to that of body B can be calculated by comparing the kinetic energy of body A (fully converted to potential energy) to the kinetic energy of body B (partially converted to potential energy).
- Since body A converts all its initial kinetic energy into potential energy at the highest point, the ratio of their initial kinetic energies will be 0:1.
In conclusion, the ratio of the initial kinetic energy of body A to that of body B is 0:1, as body A converts all its initial kinetic energy into potential energy at the highest point, while body B retains some kinetic energy due to its horizontal component of velocity.