A single roller$-$coaster car is moving with speed on the

first section of track when it descends a $5\mathrm{.}0-$m$-$deep valley, then

climbs to the top of a hill that is above the first section of

track. Assume any effects of friction or of air resistance are negligi$-$

ble. $($a$)$ What is the minimum speed required if the car is to travel

beyond the top of the hill? $($b$)$ Can we affect this speed by changing

the depth of the valley to make the coaster pick up more speed at

the bottom? Explain.