How do you explain this, Equation?

[sl02ggp]

A person who weighs 200 lbs is falling through the sky while attached to a parachute. The equation of the downward velocity as a function of time for this is:

dv/dt = g - (k/m)v

Where g is the acceleration due to gravity, m the person's mass, and k is a constant depending on the physical properties of the parachute.

Question: How does this equation physically make sense? Where does the variables from the ride hand side come from?

 

[sl02ggp]

anyone?

 

[Mark44]

A person who weighs 200 lbs is falling through the sky while attached to a parachute. The equation of the downward velocity as a function of time for this is:

dv/dt = g - (k/m)v

Where g is the acceleration due to gravity, m the person's mass, and k is a constant depending on the physical properties of the parachute.

Question: How does this equation physically make sense? Where does the variables from the ride hand side come from?

If the person were falling in a vacuum, the differential equation would be dv/dt = g. The resistance to motion caused by the parachute (and the person's body) will lessen the acceleration, which explains the (k/m)v term being subtracted on the right (not ride) side.

Is that what you're asking about?

 

[HallsofIvy]

A person who weighs 200 lbs is falling through the sky while attached to a parachute. The equation of the downward velocity as a function of time for this is:

dv/dt = g - (k/m)v

Where g is the acceleration due to gravity, m the person's mass, and k is a constant depending on the physical properties of the parachute.

Question: How does this equation physically make sense? Where does the variables from the ride hand side come from?

Experimental evidence (which is the final arbiter in "real life" matters) indicates that for an large object moving through air, the air resistance (drag) is, at least approximately, directly proportional to the speed with which the object is moving. 0 speed would mean it is not moving through the air at all so no drag. If the object were moving upward, the resistance would be downward and if the object is moving downward the resistance would be upwared- always opposite to the motion hence the "-".

Starting from "mass times acceleration = total force" we would have m(dv/dt)= mg- kv. Dividing both sides by m, dv/dt= g- (k/m)v.