Find the sum of the following four vectors ( (a) and (b) for x and y components

Question

Find the sum of the following four vectors ((a)and (b) for x and y components respectively), andas (c) a magnitude and (d) anangle relative to +x (including sign plus or minus).
P: 17 m,at 24o counterclockwise from +x
Q: 16 m,at 9.4o counterclockwise from +y
R: 23 m,at 25o clockwise from -y
S: 12 m,at 34o counterclockwise from -y

(a)

Number

Units

(b)

Number

Units

(c)

Number

Units

(d)

Number

Units

(a)

Number

Units

This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3times

Explanation / Answer

Use trig to break all into x and y components. Think of whatquadrant they're in to get + or -... Py = 17sin(24) = 6.9 Px = 17cos(24) = 15.5 Qy = 16sin(80.6) = 15.8 Qx = -16cos(80.6) = -2.6 Ry = -23sin(65) = -20.8 Rx = -23cos(65) = -9.7 Sy = -12sin(56) = -9.9 Sx = -12cos(56) = -6.7 -- Then, add up all the y's and all the x's **y = -8** **x = -3.5** For magnitude, use Pythagorean's Theorem -8^2 + -3.5^2 = c^2 **Magnitude (c) = 8.73** -- Use tangent for the angle (d). Tan(d) = -8/-3.5 d = 246.4o **With respect to +x, this is -113oclockwise** **With respect to +x, this is -113oclockwise**

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