A particle slides under gravity $g=9\mathrm{.}8\frac{m}{s^2}$ from a point $(0,b)$ to a point $(a,0)$ without friction. The fixed points are:

$(0,b)=(0,30)m,(a,0)=(40,0)m$

$(1.)$ Find the curve that minimizes the time of descent $($shortest time curve$).$

$(2.)$ Compute the time it takes for the particle to fall along this curve.

$(3.)$ Compute the time it takes for the particle to fall along the straight line connecting the two points.