An object with mass m = 0.5 kg is thrown upwards with initial velocity v0 = 20 m

Question

An object with mass m = 0.5 kg is thrown upwards with initial velocity v0 = 20 meters from the roof of a building which is 30 meters high. Assume there is a force due to air resistance that is proportional to the velocity v of the object with a positive constant of proportionality (coefficient of drag) k = 1/10 . You may use g = 10 meters per second squared as the gravitational constant.

Calculate the velocity of the object as a function of time. If the object is allowed to continue indefinitely, what would be its velocity eventually (for terminal velocity use limits.)

Explanation / Answer

we have the expression for force as

F=kv

where k is a constant of proportionality

mdv/dt =v/10

.5(dv/dt)=v/10

2dv/v =dt

integrating both side

2lnv=t+c

at t=0 v=20m/s

2ln20 =c

therefore our equation will become

2lnv =t+2ln20

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