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Q22 P

Physics For Scientists & Engineers
Found in: Page 73

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Short Answer

Use the component method to add the A vectors and B shown in Figure P3.11. Both vectors have magnitudes of 3.00m and vector A makes an angle of with the x axis. Express the resultant A+B in unit-vector notation.


See the step by step solution

Step by Step Solution

Step 1: Define the components

In a two-dimensional coordinate system, the x-component and y-component are commonly considered to be the components of a vector. It can be written as V = vx, vy with V denoting the vector.

These are the components of vectors created along the axes. In this article, we shall find the components of any given vector using formulas for both two-dimensional and three-dimensional coordinate systems.

vx=Vcos θvy=Vsin θ

Step 2: State the given data

A=3 mB=3 mθA=30°θB=90°

Step 3: Find the component vector A

Discover the following components to express A in component form:

Ax=Acos θA=3 cos30°=2.6 m

Ay=Acos θA=3 cos30°=1.5 m

A=Axi^+Ayj^=(2.6 i^+1.5j^) m

Step 4: Find the component vector B

Discover the following components to express B in component form

Bx=0 mBy=3 mB=Bxi^+Byj^=(3j^) m

Now find the resultant of A and B. We will add the components.

A+B=(2.6i^+1.5j^) m+(3j^) m=(2.6i^+4.5j^) m

The resultant vector is A+B=(2.6i^+4.5j^) m

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