Observe the resultant velocity is the vector sum of the boat velocity and the river velocity. use the principles of vector addition to determine the resultant velocity for each combination of boat/ current velocities listed below. use a sketch of the two vectors and the resultant accompanied by the use of the pythagorean theorem and trigonometric functions to determine the magnitude and direction of the resultant

Athin, square metal plate measures 14 cm on each side and has emissivity of 0.60. the plate is heated to a temperature of 745°c. what is the rate at which the plate radiates energy ? the stefan-boltzmann constant is 5.67 × 10-8 w/(m2 ? k4). remember that the plate will radiate energy from both its top and bottom surfaces.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

Since the energy was not raising the temperature of the water during these segments, what was the energy used to do instead? your answer must include an explanation of what is happening to the molecules.