Two electrons, each with mass m and charge q, are released from positions very far from each other. with respect to a certain reference frame, electron a has initial nonzero speed v toward electron b in the positive x direction, and electron b has initial speed 3v toward electron a in the negative x direction. the electrons move directly toward each other along the x axis (very hard to do with real electrons). as the electrons approach each other, they slow due to their electric repulsion. this repulsion eventually pushes them away from each other.

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?

Arock displaces 1.65 l of water. the volume of the rock is: a: 1,650 cm³ b: 165.0 cm³ c: 16.50 cm³ d: 0.165 cm³

Water flows through a garden hose which is attached to a nozzle. the water flows through hose with a speed of 2.19 m/s and through the nozzle with a speed of 19.8 m/s. calculate the maximum height (in m) to which water could be squirted if it emerges from the nozzle and emerges with the nozzle removed.