Awoman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 4.0º to the horizontal. if friction forces are ignored, how far along the hill does she travel before stopping?

The kinetic energy K = 0.5 * m * v² must be equal to the potential energy U = m * g * h.

m mass
v velocity
h height
g = 9.81m/s²

The mass m cancels out:
0.5 * v² = g * h
Solve for height h and transform to distance traveled.
(sin (4°) = height / distance)