1. A particle is projected vertically upward in a constant gravitational field with an initial speed v,. Show that if there is a retarding force proportional to the square of the instantaneous speed, the speed of the particle when it returns to the initial position V,V, is where v, is the terminal speed. Vvi + v}
1. A particle is projected vertically upward in a constant gravitational field with an initial speed v,. Show that if there is a retarding force proportional to the square of the instantaneous speed, the speed of the particle when it returns to the initial position V,V, is where v, is the terminal speed. Vvi + v}
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Transcribed Image Text:1. A particle is projected vertically upward in a constant gravitational field with an
initial speed v,. Show that if there is a retarding force proportional to the square of
the instantaneous speed, the speed of the particle when it returns to the initial position
v,v,
is
where v, is the terminal speed.
Vvi + v
Expert Solution
Concept and Principle:
If we consider the motion, the particle goes up in a retarding potential and comes back to its initial position.
The motion when the particle is going up can be written as follows:
Similarly for a downward motion,
If we take the highest point the particle reached as the starting point for downward motion, we can calculate the velocity.
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