4. A model of a bicycle is shown below. Wheel Wheel Sprocket Chain G Pedal Pedal Sprocket The pedal is attached to a sprocket. The pedal and its sprocket rotate with the same rotational velocity. This rotational velocity is the rotational velocity of your feet on the pedals. The bike's chain connects the pedal sprocket to another sprocket connected to rear wheel of the bike. The chain causes the tangential velocity of the two sprockets to be the same at their outer edge. The wheel's sprocket and the rear wheel of the bike rotate at the same rate. [15 points] a. Derive an equation for the bike's speed as a function of the rotational speed of the pedal sprocket and the radiuses of the pedal sprocket, wheel sprocket, and wheel. Use these variables for your derivation (plus any physical constants or numbers you need): rps radius of pedal sprocket rws - radius of wheel sprocket I wheel - radius of wheel @ps - angular velocity of pedal sprocket (and the pedal) Vwheel - wheel's tangential velocity (speed of the bike) Explain how you've used physics in your derivation. Do not list equations. b. Richard has a bike in his garage. The pedal sprocket has a radius of 11.4 cm the wheel sprocket has a radius of 6.35cm and the wheel has a radius of 34.3 cm. Howfast would Richard be pedaling if the bike had a speed of 6.70 m/s? [3 points]