Question

A alb at ace course consists of four legs, defined by the displacement vectors A , Β , , and D , as the drawing indicates. The magnitudes of the first three vectors are A-2.80 km, 8-5 km, and C-5.30 km. The finish line of the corse conddes with the starting line. Using the data in the drawing, find (a) the distance of the furth leg and (b) the angle θ 。 Start Units (b) Number

Answer 1

Sum of horizontal components of displacement = 0

A cos 40 - B cos 35 - C cos 23 + D cos $\theta$ = 0

2.80*cos 40 - 5*cos 35 - 5.30*cos 23 + D cos $\theta$ = 0

D cos $\theta$ = 6.8295 ........(1)

Sum of vertical components of displacement = 0

A sin 40 + B sin 35 - C sin 23 - D sin $\theta$ = 0

D sin $\theta$ = 2.80*sin 40 + 5*sin 35 - 5.30*sin 23

D sin $\theta$ = 2.5968 ............(2)

From eq (1) and (2),

tan $\theta$ = 2.5968 / 6.8295

$\theta$ = 20.82 deg

D =  6.8295 / cos (20.82)

D = 7.306 km

(a)

Distance of fourth leg = 7.306 km

(b)

angle $\theta$ = 20.82 deg