Two train whistles have identical frequencies of 1.80 ∗ 102 hz. when one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 2.00 beats per second when the whistles operate together. what are the possible speeds and directions that the moving train can have? [3.85 m/s or 3.77 m/s]

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?

If the spring constant k of a pogo stick is 3500 n m and the weight of the person on the pogo stick is 700 n, how much is the spring in the botom of the pogo stick compressed?

The radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.