Question

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to ______. [Use g = 10 ms⁻²]

Options

• 1 : 1

• `sqrt2 : sqrt3`

• `sqrt3 : sqrt2`

• 2 : 3

Answer 1

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to `bbunderline(sqrt2 : sqrt3)`.

Explanation:

Given: g = 10 ms⁻²

Gravity (mg) = 5 × 10 m/s² = 50 N

Air Resistance (F) = 10 N

Formula: Acceleration for Ascent (a_a):

`a_a = (mg + F)/m`

= `(50 + 10)/5`

= `60/5`

= 12 m/s²

Acceleration for Descent (a_d):

`a_d = (mg - F)/m`

= `(50 - 10)/5`

= 8 m/s²

The distance H is the same for both paths. Using the formula:

t = `sqrt((2 H)/a)`

∴ The time is inversely proportional to the square root of acceleration:

t α `1/sqrta`

`(t_a)/(t_d) = sqrt((a_d)/(a_a))`

= `sqrt(8/12)`

= `sqrt(2/3)`

= `sqrt2 : sqrt3`