Six runner s have the mass (in multiples of m0m_{0}m0), speed (in multiples of v0v_{0}v0), and direction of travel that are indicated in the table. Which two runners have identical momenta? (a) B and C, (b) A and C, (c) C and D, (d) A and E, (e) D and F.
RunnerMassSpeedDirection of TravelA12m0v0Due northBm0v0Due eastCm02v0Due southD2m0v0Due westEm012v0Due northF2m02v0Due west\begin{matrix} \text{Runner} & \text{Mass} & \text{Speed} & \text{Direction of Travel}\\ \text{A} & \text{}{\frac{1}{2} m_{0}} & \text{}{v_{0}} & \text{Due north}\\ \text{B} & \text{}{m_{0}} & \text{}{v_{0}} & \text{Due east}\\ \text{C} & \text{}{m_{0}} & \text{}{2 v_{0}} & \text{Due south}\\ \text{D} & \text{}{2 m_{0}} & \text{}{v_{0}} & \text{Due west}\\ \text{E} & \text{}{m_{0}} & \text{}{\frac{1}{2} v_{0}} & \text{Due north}\\ \text{F} & \text{}{2 m_{0}} & \text{}{2 v_{0}} & \text{Due west}\\ \end{matrix} RunnerABCDEFMass21m0m0m02m0m02m0Speedv0v02v0v021v02v0Direction of TravelDue northDue eastDue southDue westDue northDue west
Find the geodesics on the cone x2+y2=z2x^{2}+y^{2}=z^{2}x2+y2=z2. Hint: Use cylindrical coordinates.
A stiff, 10-cm-long tube with an inner diameter of 3.0 mm is attached to a small hole in the side of a tall beaker. The tube sticks out horizontally. The beaker is filled with 20∘C20^{\circ} \mathrm{C}20∘C water to a level 45 cm above the hole, and it is continually topped off to maintain that level. What is the volume flow rate through the tube?
At high altitudes the air is less dense. If the density of air were half that at sea level, how would d, the mean free path of an electron in air, change? (1) d would be the same. (2) d would be twice as long. (3) d would be half as long. (4) d would be 1/4 as long. (5) d would be 4 times as long.