How does the electrostatic potential energy of a system of two positive point charges change when the distance between them is tripled: (a) it is reduced to one-third its original value, (b) it is reduced to one-ninth its original value, (c) it is unchanged, or (d) it is increased to three times its original value?

Aprojectile is launched horizontally 10m above the ground and with an initial velocity of 15 m/s. a) sketch the trajectory using an appropriate coordination system. b) how long for the projectile to reach the ground. c) how far did projectile travel horizontally before striking the ground. d) determine the projectilex & y position at t-1.3s e) determine the magnitude and direction of projectile velocity at t= 1.3s f) determine the magnitude and direction of projectile acceleration at t-1.3s

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?

Compare the horizontal displacement of the two balls as they travel to the ground. what do you observe?