A 3-in-diameter horizontal jet of water, with velocity 140 ft/s, strikes a bent plate, which deflects the water by $135^{\circ}$ from its original direction. How much force is required to hold the plate against the water stream and what is its direction? Disregard frictional and gravitational effects.

Find the number of possible license plate numbers (with no letters or digits excluded) for each of the following conditions:

6 digits

A thin square plate is uniformly deformed as shown .Determine the shear strain $\gamma_{x y}$ after deformations (a) at corner $P$, and (b) at corner $Q$.

Draw a diagram comparing convection in a pot of water with convection in Earth's mantle. Relate the process of convection to plate movement.

The path of a baseball after it is hit is given by h = -0.003x$^{2}$ + 1.19x + 5.2 where h is the height (in feet) of the baseball and x is the horizontal distance (in feet) of the ball from home plate. The ball hits the top of the outfield fence that is 10 feet high. How far is the outfield fence from home plate.

To produce a polarized laser beam, a plate of transparent material is placed in the laser cavity and oriented so the light strikes it at the polarizing angle. Such a plate is called a Brewster window. Prove that if $\theta_{\mathrm{P} 1}$ is the polarizing angle for the $n_1$ to $n_2$ interface, then $\theta_{\mathrm{P} 2}$ is the polarizing angle for the $n_2$ to $n_1$ interface.

A 1-mm-thick copper plate $(k=401 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ is sandwiched between two $7$-$\mathrm{mm}$-thick epoxy boards $(k=0.26 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ that are $15 \mathrm{~cm} \times 20 \mathrm{~cm}$ in size. If the thermal contact conductance on both sides of the copper plate is estimated to be $6000 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$, find the error involved in the total thermal resistance of the plate if the thermal contact conductances are ignored.

Two triangular plates are congruent. The area of one of the plates is 60 square inches.What is the area of the other plate? Explain.

An avalanche may occur when the temperature keeps snow crystals from sticking together. The room temperature in an avalanche research lab is -30°C. Scientists study changes in snow crystals by melting snow on a hot plate that heats to only -1°C. In a regular lab, the room temperature is about 18°C and a hot plate heats to about 300°C. How many degrees warmer is the hot plate than the room temperature in each lab? Which difference is greater? How much greater?

A $\frac{1}{4}$-in steel plate having a thermal conductivity of $25 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{F}$ is exposed to a radiant heat flux of $1500 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^2$ in a vacuum space where the convection heat transfer is negligible. Assuming that the surface temperature of the steel exposed to the radiant energy is maintained at $100^{\circ} \mathrm{F}$, what will be the other surface temperature if all the radiant energy striking the plate is transferred through the plate by conduction?

A charge of $2.0 \times 10^{-10} \mathrm{C}$ is to be stored on each plate of a parallel-plate capacitor having an area of $650 \mathrm{mm}^{2}\left(1.0 \mathrm{in} .^{2}\right)$ and a plate separation of 4.0 mm (0.16 in.). (a) What voltage is required if a material having a dielectric constant of 3.5 is positioned within the plates? (b) What voltage would be required if a vacuum were used? (c) What are the capacitances for parts (a) and (b)? (d) Compute the dielectric displacement for part (a). (e) Compute the polarization for part (a).

Explain why a doctor would be worried about a child who broke a long bone close to the epiphyseal plate.

The amount of plate glass G sold can be affected by the number of new building contracts B issued and automobiles A produced, since plate glass is used in buildings and cars. A plate glass company in California wanted to forecast sales. The table contains sales data for three consecutive years. All units are in millions.

The data were modeled by

$$G=a A+b B+c,$$

where a, b, and c are constants.

Solve this linear system. Write a formula for G.

What was Wegener's hypothesis called?

A. seafloor spreading

B. plate tectonics

C. continental drift

D. slab pull