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-?

The great sandini is a 60.0-kg circus performer who is shot from a cannon (actually a spring gun). you don’t find many men of his caliber, so you him design a new gun. this new gun has a very large spring with a very small mass and a force constant of 1100 n/m that he will compress with a force of 4400 n. the inside of the gun barrel is coated with teflon, so the average friction force will be only 40.0 n during the 4.00 m he moves in the barrel. at what speed will he emerge from the end of the barrel, 2.50 m above his initial rest position?