A meteorological balloon of mass 0.2 Kg falls vertically from rest, the total resistance at V m/s is approximately (1+0.1V)N taking g=9.8 m/s^2# . Calculate: a) The terminal velocity? b) Time taken for the balloon to reach half of the terminal velocity?
2 Answers
see below
Explanation:
For motion, with positive direction vertically downwards, Newton's 2nd Law:
As
This separates:
And integrates as:
Terminal velocity
Time
The terminal velocity is
Explanation:
The mass of the balloon is
The net force on the balloon according to Newton's second law is
The acceleration due to gravity is
When the terminal velocity is reached, the velocity is constant
Therefore,
Half the terminal velocity is
The initial velocity is
Solve the differential equation
The time is