Question

A body is projected vertically up from the ground. Taking
air resistance into account, if t1 is the time taken in
going up while t2, in coming down to starting point,
then:​

Answer 1

“air resistance or air drag always opposite the body's motion.”

here a ball is projected vertically upward from ground, so air resistance acts downward on it.

Let weight of body is w and air resistance acts on it is f

then, net force acting on body , Fnet = (w + f)

so, acceleration of body, a = (w + f)/m > g , means in ascending motion, acceleration of body becomes larger than acceleration due to gravity.

so, time taken to reach extreme point , t1 = u/a = u/{(w + f)/m} .....(1)

similarly in descending motion, air resistance acts upward direction.

so, net force acting on body, Fnet = w - f

then, acceleration , a' = (w - f)/m

and now time taken by particle to reach ground , t2 = u/{(w - f)/m} ....(2)

from equations (1) and (2),it is clear that t1 < t2.

hence, relation between t1 and t2 is t1 < t2