Question to find air resistance

[siddharthmishra19]

Homework Statement

A body of mass m is dropped from a certain height without initial velocity. At the time t when its speed is v, what is the work done by the air resistance to retard the body?

Homework Equations

Laws of conservation of momentum and inertia

The Attempt at a Solution

$$E_(final) - E_(initial) = W_net$$

$$mv^2/2 - mgh = Fs = Fvt$$

Solving,

$$F = (mv^2/2 - mgh)vt$$

Something is definitely wrong... the answer is given as:

$$F = 0.5mv(gt-v)$$

 

[SGT]

Homework Statement

A body of mass m is dropped from a certain height without initial velocity. At the time t when its speed is v, what is the work done by the air resistance to retard the body?

Homework Equations

Laws of conservation of momentum and inertia

The Attempt at a Solution

$$E_(final) - E_(initial) = W_net$$

$$mv^2/2 - mgh = Fs = Fvt$$

Solving,

$$F = (mv^2/2 - mgh)vt$$

Something is definitely wrong... the answer is given as:

$$F = 0.5mv(gt-v)$$

s would be vt if the body moved with constant velocity v during the time t.
The work done by the air resistance is Fh, where F is the mean value of the air resistance.