4.I.3E
The position of the leading edge of an avalanche moving down a mountain side making a positive angle to the horizontal satisfies the equation
where is the acceleration due to gravity.
By multiplying the equation by , obtain the first integral
where is an arbitrary constant of integration and the dot denotes differentiation with respect to time.
Sketch the positive quadrant of the phase plane. Show that all solutions approach the trajectory
Hence show that, independent of initial conditions, the avalanche ultimately has acceleration .
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