09/10/2015 11:55 PM A 5/10 Gradebook Print calculator Periodic Table Question 1

Question

09/10/2015 11:55 PM A 5/10 Gradebook Print calculator Periodic Table Question 1 of 22 Map A this questionhas been astomized by Nathaniel Cunninghamat Nebraska Wesleyan University Vector C, as shown in the figure below, points in the negative ydirection, and has a magnitude 28.2 m. Vectors A and Bare at angles a 43.4 and B 25.2 above the x-axis respectively. If the vector sum A B CEO, what are the magnitudes of A and B? Number Number figure not to scale G Previous Give Up & View Solution 2 Check Answer Next Ex Hint

Explanation / Answer

write all vector in compoennt form:
Vector A = A cos 43.3 x+ A sin 43.4 y
=0.73A x + 0.69 A y

Vector B = -B cos 25.2 x+ B sin 25.2 y
= - 0.9 B x + 0.43 B y
Vector C = - 28.2 y

Vector A + Vector B + Vector C = 0
0.73A x + 0.69 A y - 0.9 B x + 0.43 B y - 28.2 y =0
(0.73A -0.9 B) x + (0.69A +0.43B-28.2) = 0
So,
0.73A -0.9 B = 0
0.69A +0.43B-28.2 = 0
Solving above 2 equations:
A = 27 and B= 22

Answer:

A = 27 m

B= 22 m

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