A projectile fired from the ground follows the trajectory given by the following equation, where vo is the initial speed, 0 is the angle of projection, g is the acceleration due to gravity, and k is the drag factor caused by air resistance. Vo cos(8) using the power series representation In(1 +xX)-x + . . .,-1 < x < 1, verify that the trajectory can be rewritten as the following. Using the power series representation ln(1 + x) = x--+ gx2 kgx3 2vo2 cos2(0) 3vo3 cos3(0) 4vo4 cos4(0) y (tan(0))x - y = ( tan(0) + w cos(0) n 1 y = tan(?)x-?

Which describes increasing the efficiency of energy resource

You have two photos of a person walking. one shows the person at the corner of third and main streets, the other shows the person at the corner of tenth and main streets. there are lampposts at every corner in this town, and the first picture shows it to be 10: 32: 00 exactly. the second picture shows it to be 10: 49: 30. you know three facts: (1) all of the clocks are synchronized; (2) there are exactly 12 equal-sized blocks per kilometer in this town; and (3) the streets that cross main in this area are numbered consecutively, with no interruptions. what is the person’s average speed in kilometers per hour?

When a lead acid car battery is recharged by the alternator, it acts essentially as an electrolytic cell in which solid lead(ii) sulfate is reduced to lead at the cathode and oxidized to solid lead(ii) oxide at the anode. suppose a current of is fed into a car battery for seconds. calculate the mass of lead deposited on the cathode of the battery.