A particle is moving in sand under acceleration `a=g-lambday^(2)`, where lambda is a positive constant and `y` is the distance traveled on the y-axis. If the initial velocity is `v_(0)` and after traveling a distance `y_(m)`, the particle stops, find `lambda` (the motion is along the y-axis).

A particle is moving in sand under acceleration `a=g-lambday^(2)`, whe

1.	A particle is moving in sand under acceleration `a=g-lambday^(2)`, where lambda is a positive constant and `y` is the distance traveled on the y-axis. If the initial velocity is `v_(0)` and after traveling a distance `y_(m)`, the particle stops, find `lambda` (the motion is along the y-axis).
Answer» `a=g-lambday^(2)` `v(dv)/(dy)=g-lambday^(2)` `int_(v_(0))^(0) v dv=int_(0)^(y_(m))(g-lambday^(2))dy` `\|v^(2)/2\|_(v_(0))^(0)=\|gy-(lambday^(3))/3\|_(0)^(y_(m))` `0-v_(0)^(2)/2=gy_(m)-(lambday_(m)^(3))/3` `(lambday_(m)^(3))/3=gy_(m)+v_(0)^(2)/2=(2g y_(m)+v_(0)^(2))/2` `lambda=(6 g y_(m)+3v_(0)^(2))/(2 y_(m)^(3))`

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A particle is moving in sand under acceleration `a=g-lambday^(2)`, where lambda is a positive constant and `y` is the distance traveled on the y-axis. If the initial velocity is `v_(0)` and after traveling a distance `y_(m)`, the particle stops, find `lambda` (the motion is along the y-axis).

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