Respuesta :
Because the diver is at terminal velocity, there is no change in velocity. But because there is still a force applied but no change in velocity, that means that there is an equal force applied in the opposite direction. That means the Force of the drag is equal to the force of gravity.
The work done by the drag force on the skydiver over the distance [tex]d[/tex] is [tex]\boxed{\dfrac{1}{2}m{v^2} - mgd}[/tex].
Further Explanation:
The skydiver dives from the hot air balloon and falls freely under gravity and attains the terminal velocity. The skydiver attains the kinetic energy and some of the energy attained is lost in overcoming the drag force.
The amount of energy lost by the skydiver is the work done by the drag force.
The kinetic energy of the skydiver as he falls with speed [tex]v[/tex] is:
[tex]KE = \dfrac{1}{2}m{v^2}[/tex]
The potential energy lost by the skydiver due to the decrease in height is:
[tex]PE = mgd[/tex]
Therefore, according to work energy theorem, the amount of work done by drag force is equal to the change in energy.
[tex]{W_D} = KE - PE[/tex]
Here, [tex]{W_D}[/tex] is the work done by the drag force.
Substitute the values of [tex]KE[/tex] and [tex]PE[/tex] in above expression.
[tex]{W_D} = \Dfrac{1}{2}m{v^2} - mgd[/tex]
Thus, the work done by the drag force on the skydiver over the distance [tex]d[/tex] is
[tex]\boxed{\dfrac{1}{2}m{v^2} - mgd}[/tex]
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Answer Details:
Grade: Senior School
Subject: Physics
Chapter: Conservation of Energy
Keywords: Skydiver, terminal velocity, drag force, work energy theorem, work done, magnitude, air drag, acceleration due to gravity.
