contestada

Vector c has a magnitude 25.8 m and is in the direction of the negative y-axis. vectors a and b are at angles α = 45.4° and β = 28.2° up from the x-axis respectively. if the vector sum a b c = 0, what are the magnitudes of a and b?

Respuesta :

As per given in above equation we can say

[tex]\vec a + \vec b + \vec c = 0[/tex]

so in X direction

[tex]a cos 45.4 = b cos28.2[/tex]

[tex]a = 1.255 b[/tex]

in Y direction

[tex]a sin45.4 + b sin28.2 = 25.8[/tex]

[tex]1.255 b * 0.712 + 0.472 *b = 25.8[/tex]

[tex]b = 18.9 m[/tex]

also now for a we have

[tex]a = 1.255 * 18.9 = 23.7 m[/tex]

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