A commuter airplane starts from an airport and takes the route shown in the figu

Question

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0 degree north of east. Next, it flies for 150 km 20.0 degree west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point. distance km angle degree weight of north Assume it takes 8.35 minutes to fill a 25.0 gal gasoline tank. (1 U.S. gal = 231 in.^3) (a) Calculate the rate at which the tank is filled in gallons per second. gal/s (b) Calculate the rate at which the tank is filled in cubic meters per second. m^3/s (c) Determine the time interval, in hours, required to fill a 1.00-m volume at the same rate. hr

Explanation / Answer

Problem 23)

The component of the resultant vector equals the sum of that component of the added vectors;

Rx = (A+B+C)x = Ax + Bx + Cx .................(1)

Ry = (A+B+C)y = Ay + By + Cy ............... (2)

ax = acosx = 175 cos30° = 175 x 0.866 = 152 km

ay = asiny = 175 sin30° = 175 x 0.500 = 87.5 km

bx = bsinx = -150 sin20° = -150 x 0.342 = -51.3 km

by = bcosy = 150 cos20° = 150 x 0.940 = 141 km

cx = ccosx = 190 cos180° = 190 x (-1) = - 190 km

cy = csiny = 190 sin180° = 0

Rx = 152 - 51.3 - 190 = -89.3 km

Ry = 87.5 + 141 + 0 = 229 km

R = sqrt(Rx2 + Ry2) = sqrt(89.32 + 2292) = sqrt(7974.5 + 52441) = sqrt(60415) = 246 km

Theta = tan-1(Ry / Rx) = tan-1(229/-89.3) = tan-1(-2.564) = 90° -39° = 51° to x - axis

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