Acat’s crinkle ball toy of mass 15g is thrown straight up with an initial speed of 3m/s . assume in this problem that air drag is negligible.

(a) what is the kinetic energy of the ball as it leaves the hand?
(b) how much work is done by the gravitational force during the ball’s rise to its peak?
(c) what is the change in the gravitational potential energy of the ball during the rise to its peak?
(d) if the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when it reaches the maximum height?
(e) what if the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy be when it leaves the hand?
(f) what is the maximum height the ball reaches?

Light that is polarized along the vertical direction is incident on a sheet of polarizing material. only 96% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. no light passes through the second sheet. what angle does the transmission axis of the second sheet make with the vertical?

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?

The uniform slender bar rests on a smooth horizon- tal surface when a force f is applied normal to the bar at point a. point a is observed to have an initial acceleration aa of 20 m/s2, and the bar has a corre- sponding angular acceleration of 18 rad /s2. deter- mine the distance b.