The maximum height reached by the ball is 20 meters.
By the principle of energy conservation, total mechanical energy of the ball ([tex]E[/tex]) is conserved in every time and part of the motion and that energy is the sum of the gravitational potential energy ([tex]U[/tex]) and the translational kinetic energy ([tex]K[/tex]). All energy components are measured in joules.
Please remind that gravitational potential energy is directly proportional to the height of the ball ([tex]z[/tex]), in meters. Then, the total energy and the maximum height reached by the ball are, respectively:
[tex]E = U + K[/tex] (1)
[tex]E = 100\,J[/tex]
[tex]\frac{100\,J}{50\,J} = \frac{z}{10\,m}[/tex] (2)
[tex]z = 20\,m[/tex]
The maximum height reached by the ball is 20 meters.
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The maximum height reached by the ball is 20 m.
Given data:
The height above the ground is, h = 10 m.
The potential energy is, PE = 50 J.
The kinetic energy at ground is, KE = 50 J.
According to conservation of energy, "The total mechanical energy is equal to sum of kinetic energy and potential energy at any point".
ME = KE + PE
ME = 50 J + 50 J
ME = 100 J.
Since, at maximum height, the entire mechanical energy is due to potential energy at that point .
Mechanical energy at maximum height = potential energy at maximum height
ME = PE'
ME = mgH ........................................(1)
Here m is the mass of body,
[tex]PE = mgh\\50 = m \times 9.8 \times 10\\m = 0.51 \;\rm kg[/tex]
Substituting the value in equation (1) as,
[tex]100 = 0.51 \times 9.8 \times H\\H= \dfrac{100}{0.51 \times 9.8} \\H = 20 \;\rm m[/tex]
Thus, the maximum height reached by the ball is 20 m.
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