A body fired vertically up reaches a maximum heigh H where is kinetic energy 75% of potential energy
To find the maximum height reached by the body fired vertically up, we need to understand the relationship between kinetic energy and potential energy.
When the body is at its maximum height, its gravitational potential energy is maximum, and its kinetic energy is minimum because it momentarily comes to a stop before falling back down due to gravity.
The total mechanical energy (E) of the body remains constant throughout its motion, as there are no external forces acting on it. It can be expressed as the sum of kinetic energy (KE) and potential energy (PE):
E = KE + PE
Given that the kinetic energy at the maximum height is 75% of the potential energy, we can write:
KE = 0.75 * PE
Substituting this into the previous equation:
E = 0.75 * PE + PE
E = 1.75 * PE
Since the total mechanical energy is constant, it is equal to the initial gravitational potential energy at the starting point, which is at ground level:
E = PE_initial
Substituting this into the equation:
PE_initial = 1.75 * PE
At ground level, the gravitational potential energy of an object is given by:
PE = m * g * h
Where m is the mass of the object, g is the acceleration due to gravity, and h is the height from the ground.
Combining the equations:
PE_initial = 1.75 * m * g * h
Simplifying:
h = PE_initial / (1.75 * m * g)
Therefore, to find the maximum height (H) reached by the body, we need to know the initial gravitational potential energy (PE_initial), mass (m), and acceleration due to gravity (g).