The brewing temperature of the water used is very important. It should be between 195 F and 205 F. The closer to 205 F the better. Boiling water (212 F) should never be used, as it will burn the coffee. Water that is less than 195 F will not extract properly. On the other hand, coffe that has a temperature of 205 F is too hot to drink. 6 Coffee best when it is served at a temperature of 140 F to 155 F (the Goldilocks range). (a) Suppose coffee is initially brewed at 205 F. If room temperature is 70 F, set up an initial-value problem to model the temperature of the coffee at time t, where t is the time in minutes after brewing has finished.
(b) Solve the initial-value problem from Task 1.2.2.a
(c) If the temperature of the coffee drops from 205 F to 200 F in the first two minutes after brewing, how long before the coffee reaches a temperature of 155 F?

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?

The rocket is fired vertically and tracked by the radar station shown. when θ reaches 66°, other corresponding measurements give the values r = 32700 ft, r¨ = 85 ft/sec2, and θ˙ = 0.019 rad/sec. calculate the magnitudes of the velocity and acceleration of the rocket at this position.

Awater-filled u-tube manometer is used to measure the pressure inside a tank that contains air. the water level in the u-tube on the side that connects to the tank is 5 ft above the base of the tank. the water level in the other side of the u-tube (which is open to the atmosphere) is 2 ft above the base. determine the pressure within the tank.