You and an archeologist companion, having escaped from confinement by international antiquities mobsters, are attempting to flee through underground tunnels. from your starting point in a dungeon below a ruined palace you have traveled 150 m 37° east of north, then turned left right angle and traveled 200 m further along a differ- by a ent tunnel. you now see a ladder leading to a ground-level exit. you know that a 30-m wide river runs due east past the palace, and the nearest point on its bank is 205 m due north of the dungeon. is the ground-level exit you see hid- den in the woods across the river from the palace the exposed plairn between the palace and the river? calcu- late quickly-your life may depend on the answer! (hint: note that just calculating your distance from the dungeon is not enough to ensure your safety. why?

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?

Students design a model roller-coaster track. they place a rubber ball at the highest point on the track and let it go. the ball rolls along the track pulled only by the force of gravity. eventually, it comes to a stop. which change to the design will result in the ball moving the greatest distance?

Aria drove to the store, did some shopping, and then came home. during maria's trip, when was her displacement equal to zero?