Suppose you throw a ball straight upward; it rises, then returns to your hand (a) Calling the point where it leaves your hand the origin and upward positive, make a plausible sketch of its position (vertical height) x(t) versus time t from the instant after it leaves your hand till the instant before it reaches it again.
(b) From your x(t) plot, make a sketch of the ball’s velocity v(t) versus time.
(c) From your velocity plot, sketch a plot of the ball’s acceleration versus time.
(d) Does your plot suggest that the ball’s acceleration is zero at the top of its flight?

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?