Laura is at the top f a snow-covered hill ready to slide down on her first skiing attempt. if the slope is angled at 30 degrees with respect to the horizontal, how much time passes before she reaches v=100km/h? what distance along the slope would she have covered in that time?

Assuming absence of friction or any other resistance, the component of acceleration along the slope due to gravity for a 30° slope is a= gsin(30°) m/s², where g=9.8 m/s².

Initial velocity, v0 = 0 m/s
final velocity, v = 100 km/s = 100/3.6 m/s
acceleration, a = g*sin(30°)
Distance travelled, S = to be solved.

Use the relation
v²-v0² = 2*a*S
solve for S.