A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0º to the horizontal.If friction forces are ignored,how far up the hill does she travel before stopping?
A)5.1 m
B)30 m
C)97 m
D)10 m
E)The answer depends on the mass of the woman.

Question

Quizplus · Accepted Answer

We can use conservation of energy to solve this problem. Initially, the woman has kinetic energy given by KE = (1/2)mv^2, where m is her mass and v is her initial velocity of 10 m/s. When she reaches the top of the hill, her kinetic energy will be zero, and all of her initial kinetic energy will have been converted into potential energy given by PE = mgh, where h is the height she has traveled up the hill.

To find h, we need to know the vertical component of her initial velocity. This is given by v*sin(theta), where theta is the angle of the hill. Therefore, the initial potential energy is mgh = (1/2)mv^2*sin^2(theta), so h = (1/2)v^2*sin^2(theta)/g. Plugging in the given values, we get:

h = (1/2)*(10 m/s)^2*sin^2(3.0º)/(9.81 m/s^2)
h ≈ 97 meters

Therefore, the woman travels 97 meters up the hill before stopping.

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