Aprojectile 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 + . < 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 = -?

What is the length x of the side of the triangle below? (hint: use the cosine function)

Which features on mars point to the possibility of liquid water on the planet? impact craters with sharp rims volcanic cones with craters gullies and stream-like channels mountain ranges with faults

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.