PLEASE FIND #$1$ & #$2$ BELOW.

The body falling with speed $v_0$ strikes and maintains contact with the platform supported by a nest of springs. The acceleration of the body after impact is $a=g-cy,$ where $c$ is a positive constant and $y$ is measured from the original platform position. If the maximum compression of the springs is observed to be $y_m,$ determine the constant c

PLEASE FIND THESE TWO BELOW.

$1.$ Find an expression for the velocity of the particle as a Function of $y,c,g,$ and $v_0.$

$2.$ Determine the constant $c$ as a function of $v_0,g,$ and

$y_m$