Respuesta :
if we take ball then the Kinetic Energy of the ball is ½mV²
as it rolls up the slope, the Kinetic Energy is converted to potential energy, PE = mgh.
mgh = ½mV²
h = V²/2g
The ball will rise to a maximum height of [tex]\boxed{h=\dfrac{v^2}{2g}}[/tex].
Explanation:
The kinetic energy of a body is the energy associated with the body by virtue of its motion whereas the potential energy of the body is the amount of energy stored in a body by virtue of its position.
The amount of kinetic energy stored in a body is given by:
[tex]\boxed{K=\dfrac{1}{2}mv^2}[/tex] ...... (1)
Here, [tex]K[/tex] is the kinetic energy, [tex]m[/tex] is the mass and [tex]v[/tex] is the speed of the body.
The potential energy stored in a body as it reaches its maximum height is given as:
[tex]\boxed{P=mgh}[/tex] ...... (2)
Here, [tex]P[/tex] is the potential energy stored, [tex]g[/tex] is the acceleration due to gravity and [tex]h[/tex] is the height attained by the body.
According to the conservation of energy, the energy can neither be created nor destroyed. It can only be converted from one form to another.
[tex]\text{kinetic energy}=\text{potential energy}[/tex]
Substitute the values of kinetic energy and potential energy and simplify the expression for the maximum height.
[tex]\begin{aligned}\dfrac{1}{2}mv^{2}=&mgh_{max}\\h_{max}=&\dfrac{v^2}{2g}\end{aligned}[/tex]
Therefore, the maximum height attained by the ball as it rises up is [tex]\boxed{h_{max}=\dfrac{v^2}{2g}}[/tex].
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Answer Details:
Grade: Senior School
Subject: Physics
Chapter: Conservation of Energy
Keywords:
Ball is launched, ground level, conservation of energy, kinetic, potential energy, motion, maximum height, in contact with hill, vertical height, in terms of v and g.
