The movie "The Gods Must Be Crazy" begins with a pilot dropping a bottle out of an airplane. A surprised native below, who thinks it is a message from the gods, recovers it. If the plane, from which the bottle was dropped was flying at an altitude of 500. m, and the bottle lands 400.m horizontally from the initial dropping point, how fast was the plane flying when the bottle was released? Please show work.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. a) what is the block's initial mechanical energy? b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

The electric field direction is defined by the direction of the force felt by (select one of the following answers): 1. a negative charge. 2. a positive charge. 3. both positive and negative charges.