A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0^o to the horizontal. If friction forces are ignored, how far up the hill does she travel before stopping?

Question

Quizplus · Accepted Answer

The horizontal velocity of the woman remains constant because there is no friction. Therefore, the only force acting on the woman is the gravitational force which is parallel to the incline. The force perpendicular to the incline is balanced by the normal force from the incline, so it does not affect the motion. Therefore, the motion of the woman is along the incline and can be analyzed using one-dimensional kinematics.

The initial velocity of the woman is 10 m/s, and the final velocity is 0 m/s. The acceleration is due to gravity and is given by a = g sin(3.0°), where g is the acceleration due to gravity (9.81 m/s^2). The distance traveled is given by:

Δy = (v_f^2 - v_i^2) / (2 a)

Substituting the values, we get:

Δy = (0^2 - 10^2) / (2 * 9.81 * sin(3.0°)) = 96.7 m

Rounding to the nearest whole number, the answer is 97 m. Therefore, the best choice is C. The mass of the woman does not affect the motion because the acceleration due to gravity is independent of mass.

A Woman on a Bicycle Traveling at 10 M/s on a Horizontal