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IfVx=9.80unitsandVy=-6.40units, determine the magnitude and direction ofV.

Short Answer

Expert verified

The magnitude of Vis 11.70 units, and Vis oriented at an angle of -33.15°with +X-axis.

Step by step solution

01

Step 1. Understanding the magnitude of a vector

The magnitude of a vector represents its length graphically.

02

Step 2. Given data and assumption

The magnitude of the X-component of V,Vx=9.80units

The magnitude of the Y-component of V, Vy=-6.40units

Let the magnitude of Vbe V.

03

Step 3. Calculating the magnitude of V→

For two vectors Aand B, oriented at angleθ with respect to each other, the magnitude of their resultant vector or their vector sum is given by the formula

R=A2+B2+2ABcosθ.

Here, A and B are magnitudes of vectors A and B, respectively, andR is the magnitude of the resultant vector.

In this problem, Vxand Vyare the rectangular components of V. The angle between them is 90°.

Using the formula for magnitude of vector sum, you get

V=Vx2+Vy2+2VxVycos90°=9.802+6.402=11.70units.

Thus, the magnitude of Vis 11.70 units.

04

Step 4. Calculating orientation with respect to the X-axis

The tangent function of angle θcan be written as tanθ=VyVx.

Substituting the values,

θ=tan-1-6.409.80=-33.15°.

Thus, Vis oriented at an angle of -33.15°with respect to the positive direction of the X-axis. Here, the negative sign indicates that the angle is measured clockwise from the positive X-axis.

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