A girl and her bicycle have a total mass of 40 kg. At the top of the hill her speed is 5.0 m/s. The hill is 10 m high and 100 m long. If the force of friction as she rides down the hill is 24 N, what is her speed at the bottom?Select one:a.10 m/sb.5.0 m/sc.11 m/sd.She stops before she reaches the bottom.

To solve this problem, we need to use the principle of conservation of energy. The total energy at the top of the hill (potential energy + kinetic energy) should be equal to the total energy at the bottom of the hill (kinetic energy + work done against friction).

1. Calculate the potential energy (PE) at the top of the hill using the formula PE = mgh, where m is the mass (40 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the hill (10 m). PE = 40 kg * 9.8 m/s² * 10 m = 3920 J.

2. Calculate the kinetic energy (KE) at the top of the hill using the formula KE = 0.5 * m * v², where m is the mass (40 kg) and v is the velocity (5.0 m/s). KE = 0.5 * 40 kg * (5.0 m/s)² = 500 J.

3. The total energy at the top of the hill is the sum of the potential and kinetic energy: 3920 J + 500 J = 4420 J.

4. Calculate the work done against friction as the girl rides down the hill. Work done = force * distance = 24 N * 100 m = 2400 J.

5. The total energy at the bottom of the hill is the total energy at the top minus the work done against friction: 4420 J - 2400 J = 2020 J.

6. This remaining energy is the kinetic energy at the bottom of the hill, so we can set it equal to the formula for kinetic energy and solve for v: 2020 J = 0.5 * 40 kg * v². Solving for v gives v = sqrt((2 * 2020 J) / 40 kg) = 10 m/s.

So, the girl's speed at the bottom of the hill is 10 m/s. The correct answer is a. 10 m/s.