the two vectors and in Fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30° and 105°. Find the (a) x and (b) y components of their vector sum r, (c) the magnitude of r, and (d) the angle r makes with the positive direction of the x axis.

Question

Physics

Kirsten House

20 December, 03:21

the two vectors and in Fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30° and 105°. Find the (a) x and (b) y components of their vector sum r, (c) the magnitude of r, and (d) the angle r makes with the positive direction of the x axis.

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Answers (1)

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Ayla Crawford · Answer 1

For rectangular components:

Ax = Acostheta

= 10 x cos30

= 8.66

Ay = Asintheta

= 10 x sin30

=5.

Bx = Bcostheta

= 10 x cos105

= - 2.58

By = Bsin105

= 10 x sin105

= 9.65

For magnitude of R:

A = Ax + Ay

= 8.66 + 5

= 13.66

B = Bx + by

= - 2.58 + 9.65

= 7.07

R = sq A*2 + B*2

= 15.38