Answer to Question #58203 in Mechanics | Relativity for Nayan Jyoti Das

Question

2. A paratrooper weighing 80 kg jumps with zero velocity from an aeroplane at a height of
3000 m. The air resistance encountered by the paratrooper is 2 R(t) =15v(t)^2 N where v(t)
is the velocity of the paratrooper at time t. Calculate the time required by the paratrooper
to land and the velocity at landing.

3. A mass of 2 kg is fixed to an end of a spring with spring constant k = 128 Nm^−1 and the
system is placed inside a fluid. It is set into vibration from its equilibrium position with
an initial speed of 0.6 ms^−1. If the damping force due to the fluid is 40v(t) N where v is
the instantaneous speed of the mass, determine the position of the mass as a function of
time t.

4. Use the power series method to obtain one solution of the following ODE:
x^2 y'' + 3y' - xy=0