Questions: Find the (x)-component of this vector:

Find the (x)-component of this vector:
Transcript text: Find the $x$-component of this vector:
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Solution

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Solution Steps

Step 1: Identify the given values

The magnitude of the vector \( |V| \) is 47.3 m, and the angle \( \theta \) with the horizontal axis is 39.4°.

Step 2: Use the cosine function to find the x-component

The x-component of the vector \( V_x \) can be found using the cosine function: \[ V_x = |V| \cos(\theta) \]

Step 3: Calculate the x-component

Substitute the given values into the equation: \[ V_x = 47.3 \cos(39.4°) \]

Step 4: Perform the calculation

Using a calculator to find the cosine of 39.4° and then multiplying by 47.3: \[ \cos(39.4°) \approx 0.774 \] \[ V_x = 47.3 \times 0.774 \approx 36.6 \, \text{m} \]

Final Answer

\[ V_x \approx 36.6 \, \text{m} \]

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