A girl and her bicycle have a total mass of 42 kg.At the top of the hill her speed is 4.00 m/s.The hill is 14.3 m high and 112 m long.If the force of friction as she rides down the hill is 20 N,what is her speed at the bottom?

Question

Quizplus · Accepted Answer

First, we need to determine the potential energy at the top of the hill:
PE = mgh = 42 kg * 9.81 m/s^2 * 14.3 m = 5802.18 J

Next, we need to find the work done by friction:
Wfriction = f * d = 20 N * 112 m = 2240 J

The total energy at the top of the hill equals the kinetic energy at the bottom of the hill plus the work done by friction:
PE = KE + Wfriction
KE = PE - Wfriction
KE = 5802.18 J - 2240 J = 3562.18 J

Finally, we can use the kinetic energy formula to find the velocity at the bottom of the hill:
KE = 1/2mv^2
v = sqrt((2KE)/m)
v = sqrt((2*3562.18 J)/(42 kg))
v ≈ 13.8 m/s

Therefore, the best choice is C, 13.8 m/s.

A Girl and Her Bicycle Have a Total Mass of 42