Could you help me solve this physics problem? please have the writing neatly, or

Question

Could you help me solve this physics problem?

please have the writing neatly, or typed, thank you by a lot!!!!!

1 Vectors 1.1 Tilted Axes a. Find the length of the vector and its angle with respect to the drawn x-axis: +16 m +3 m 5 m -12 m Use 2 significant digits in your final answers (calculating how uncertainty propagates through trig functions requires calculus and is beyond the scope of this class). Show all your work, including units. b. This tilted axis is defined to be the usual x and y coordinates rotated 70° counter- clockwise. Find the components of the vector above in the usual x and y coordinates

Explanation / Answer

From the given vector diagram

a)

Let R be the vector of addition of two vectors A,B

now the vector A = (-5-(-12)m)i + 0 j = 7 i + 0 j

B = (0 i + (16-3) j = 0 i + 13 j

the resultant vector is

R = (Ax+Bx) i + (Ay+By) j

R = (7+0)i + (0+13)j = 7 i + 13 j

the magnitude of R is = sqrt(7^2+13^2) = 14.76 m

the direction is thet = arc tan (13/7) = 61.70 degrees

b)

if the axis is rotated through 70 degrees counter clockwise direction then

the components of the vector R is

Rx = R cos theta , Ry = R sin theta

Rx = 14.76 cos(61.7+70) m , = -9.81 m

Ry = 14.76 sin(61.7+70) m , = 11.02 m

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