Apilot loses control of her drone and it goes into a spiraling freefall toward the ground. assume the position of the drone, relative to the pilot (consider her the 'origin') is given by ) (3sin(rt) 3cos(rt),120-9r), over [0, t,], wheret, is time until impact (t is in seconds and each component is measured in feet) a. find the velocity and acceleration vectors of the plane's trajectory determine the plane's speed at 3 seconds, as well as its downward velocity at that time (note that this is just how fast the drone's height is dropping b. assuming the pilot cannot correct the spin, determine the point on the ground (relative to our origin) where the drone hits. also determine the total distance covered by the spiraling drone (you may need to use technology here) c. assume now, on the other hand, that the drone comes out of its spiral after 8 seconds, but that its path afterward is tangent to its trajectory at that moment. determine how far from the pilot the drone hits the ground d. assume the ground is flat as far as the eye can see (as flat as, the xy-plane)

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?