Police radars detect the speed of cars in the following way: microwaves of a known frequency are shot at the car, they reflect off of the target vehicle, and return wo the police radar with a different frequency these received waves are interfered with an identical wave to the original wave sent out of the gun, and the beat frequency is measured. for this problem assume all motion is one dimensional, this way we can ignore transverse doppler shifts a) show that the wave, when is gets back to the radar is given as c+v where v is the relative motion between the police radar and the targeted car. hint: there wil be two doppler shifts that occur in this problem b) since cars, more often than not, are n(t traveling very fast u 《 c , show that the beat frequency beat i fo can be written as: 1 fbeat 2-fo hint: you may need to do a maclaurin expansion somewhere in this part. c) what is the measured beat frequency for a relative velocity of v 30 10.0 ghz?

Avery hard rubber ball (m = 0.5 kg) is falling vertically at 4 m/s just before it bounces on the floor. the ball rebounds back at essentially the same speed. if the collision with the floor lasts 0.05 s, what is the average force exerted by the floor on the ball?

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?

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