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# Repeat Question 30 taking air resistance into account. Again, give qualitative answers.

Jitender Pal
6 years ago
Assumption:
Both the ball experiences the same acceleration in the upward direction because of the presence of air resistance.
The change in velocity of the first ball is given as:

Here, g is the free fall acceleration and aR is the dacceleration ue to air resistance.
Integrate above expression under the limit that the initial velocity of the first ball at t = 0 is 0 m / s whereas the final velocity of the ball at time t is v1 :

It is important to note that the acceleration due to air resistance is dependent on time, therefore the above integral can be written as:
 …… (1)

Similarly, the change in velocity of the second ball, released one second later can be written as:

Integrate above expression under the limit that the initial velocity of the second ball at t = 0 is 0 m / s whereas the final velocity of the ball at time is t – 1 is v2 :

 …… (2)

It is important to note that when the first ball has travelled for time t , the second ball has travelled for time t – 1.
Subtract equations (1) and (2),



It is obvious that the value of integral would be greater than the value of integral , as a result, the difference v1 – v2 would be less than g (1 sec). Therefore, the objects will come closer to each other over time.