Question

A cyclist is coasting at 15 m/s when she starts down a 420 m long slope that is 30 m high. the cyclist and her bicycle have a combined mass of 70 kg . a steady 13 n drag force due to air resistance acts on her as she coasts all the way to the bottom. part a what is her speed at the bottom of the slope? express your answer with the appropriate units.

Answer 1

To find the cyclist's speed at the bottom of the slope, we use energy conservation and the work-energy theorem, considering her initial kinetic energy, potential energy due to height, and work done against air resistance.

Step-by-step explanation:

To determine the cyclist's speed at the bottom of the slope, we can use the principles of energy conservation and the work-energy theorem. The cyclist possesses initial kinetic and potential energy at the top of the slope. As she coasts down, she converts potential energy into kinetic energy while also losing some energy due to the air resistance acting as a drag force.

Step-by-Step Calculation

1. Calculate initial kinetic energy (KE1) using KE = (1/2)mv2, where m is mass and v is velocity.
2. Calculate potential energy (PE) at the top of the slope using PE = mgh, where m is mass, g is the acceleration due to gravity (9.81 m/s2), and h is the height of the slope.
3. Calculate work done against air resistance using W = Fd, where F is the drag force and d is the distance of the slope.
4. The total energy at the bottom (E2) will be the initial total energy (KE1 + PE) minus the work done against air resistance (W).
5. Solve for the final kinetic energy (KE2) at the bottom by equating it to E2.
6. Finally, use KE2 to solve for the final velocity (v2) at the bottom using the rearranged kinetic energy formula: v2 = sqrt((2 * KE2) / m).