To solve this problem we will apply the concepts related to energy conservation. So that the initial energy on the system is equivalent to the final energy.
The initial or final energy will also be the TOTAL mechanical energy of the body.
In the case of the initial energy we will have two types of energy on the body: Kinetic energy and potential energy.
For the case of the final energy we will only have the potential energy in terms of the height [tex]h_m[/tex], the mass m, and the gravity g
[tex]E_i = E_f[/tex]
[tex]KE_i + PE_i = PE_f[/tex]
[tex]\frac{1}{2} mv_0^2 +mgh_0 = mgh_m[/tex]
[tex]E = mgh_m[/tex]
The total mechanical energy will be equivalent in the terms required, to the final potential energy.
The total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g is [tex]mgh_m[/tex].
The given parameters;
The total mechanical energy of the ball is the sum of the kinetic energy and potential energy.
E = K.E + P.E
At maximum height, the velocity of the ball will be zero and the ball will have only potential energy.
The total mechanical energy of the ball at the maximum height is calculated as;
M.A = P.E
[tex]E = mgh_m[/tex]
where;
Thus, the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g is [tex]mgh_m[/tex].
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