Question

A ball is thrown vertically upward and if the air resistance has to be taken in account, would the time of rising be greater or that of fall?

Answer 1

Given : A ball is thrown vertically upward and if the air resistance has to be taken in account.

To check : would the time rising be greater or that of fall ?

Solution : air resistance just opposes the relative motion of object.

if body moves upward, air resistance acts downward and if body moves downward, air resistance acts upward.

when ball is thrown vertically upward.

a_net = -(a + g)

time taken to reach the highest point, t₁ = √{2h/(a + g)}

when ball is fallen vertically downward,

a_net = -(g - a)

time taken to reach the ground , t₂ = √{2h/(g - a)

it is clear that, t₁ < t₂

Therefore time of rising be lesser than that of falling.