Home
Class 12
MATHS
The velocity v, of a parachute falling v...

The velocity v, of a parachute falling vertically satisfies the equation `v(dv)/(dx)=g(1-v^(2)/(k^(2)))`, where g and k are constants. If v and x are both initially zero, find v in terms of x.

Text Solution

Verified by Experts

The correct Answer is:
`v^(2)= k^(2) (1-e^((-2gx)/(k^(2))))`
Promotional Banner

Topper's Solved these Questions

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.6|8 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.7|15 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 10.4|10 Videos

  • MODEL QUESTION PAPER -1

    PREMIERS PUBLISHERS|Exercise Part -IV|20 Videos

  • PROBABILITY DISTRIBUTIONS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

Similar Questions

Explore conceptually related problems

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation (d V(t)/(dt)=-k(T-t) , where k"">""0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is : (1) T^2-1/k (2) I-(k T^2)/2 (3) I-(k(T-t)^2)/2 (4) e^(-k T)

The velocity v of a particle at time t is given by v = a t + \frac { b } { t + c } where a, b and c are constant. The dimensions of a, b and c respectively are

The solution of (d v)/(dt)+k/m v=-g is

One mole of an ideal gas undergoes a process p=(p_(0))/(1+((V)/(V_(0)))^(2)) where p_(0) and V_(0) are constants. Find temperature of the gas when V=V_(0) .

The velocity v and displacement x of a particle executing simple harmonic motion are related as v (dv)/(dx)= -omega^2 x . At x=0, v=v_0. Find the velocity v when the displacement becomes x.

If F is the constant force generated by the motor of an automobiles of mass M, its velocity V is given by M(dV)/(dt)=F-kV , where k is a constant. Express V in terms of t given that V = 0 when t = 0.

The frequency of vibration v of mass m suspended from a spring of spring constant k is given by f=cm^(x)k^(y) where c is a dimensional constant. The volumes of x and y are :