Question

The helium balloon shown below is tethered by the ropes AB, AC and AD. The tension in rope AD is 990 N.
a) Write unit vectors for the directions AB and AC.
b) Express the force in rope AD as a Cartesian vector.

The helium balloon shown below is tethered by the ropes AB, AC and AD. The tension in rope AD is 990 N. a) Write unit vectors for the directions AB and AC. b) Express the force in rope AD as a Cartesian vector c) Find the magnitude of the projection of the 990 N force along the AC axis. UF 5.6 m 1.83 m 4.20 m 3.19 m 4.20 m 2.40 m

Answer 1

The coordinates of points are: - A equiv (0, 0, 5.6) C equiv (4.2, 2.4, 0) B equiv (0, - 4.2, 0) D equiv (- 3.19, 1.83, 0) vec AB = < 0, - 42, 0 > - (0, 0, 5.6 > = < 0, - 4.2, - 5.6 > so, the unit vector along this is: - hat AB = vec AB/ Vertical-bar vec AB Vertical-bar = < 0, - 4.2, - 5.6 > /squareroot (0)^2 + (- 4.2)^2 + (- 5.6)^2 = < 0, - 4.2, - 5.6 > /7 = < 0, - 0.6, - 0.8 > similarly vec AC = < 4.2, 2.4, 0 > - < 0, 0, 5.6 > = < 4.2, 2.4, - 5.6 > so, the unit vector along this is: - hat AC = vec AC/ Vertical-bar vec AC Vertical-bar = < 4.2, 2.4, - 5.6 > /squareroot (4.2)^2 + (2.4)^2 + (- 5.6)^2 = < 4.2, 2.4, - 5.6 > /7.4 = < 21/37, 12/37, - 28/37 > \r\n Thus the unit vector are: - hat AB = 0 hat i - 0.6 hat j - 0.8 hat k and hat AC = 21/37 hat i + 12/37 hat j - 28/37 hat k vec AD = < - 3.19, 1.83, 0 > - < 0, 0, 5.6 > = < - 3.19, 1.83, - 5.6 > so, hat AB = vec AD/ Vertical-bar vec