Question Video: Calculating the Horizontal Component of a Vector | Nagwa Question Video: Calculating the Horizontal Component of a Vector | Nagwa

# Question Video: Calculating the Horizontal Component of a Vector Physics • First Year of Secondary School

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The diagram shows a vector, 𝐀, that has a magnitude of 55. The angle between the vector and the 𝑥-axis is 82°. Work out the horizontal component of the vector. Give your answer to the nearest whole number.

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### Video Transcript

The diagram shows a vector, 𝐀, that has a magnitude of 55. The angle between the vector and the 𝑥-axis is 82 degrees. Work out the horizontal component of the vector. Give your answer to the nearest whole number.

In this question, we are being asked to solve for the horizontal component of the vector 𝐀. We can label this component 𝐴 subscript 𝑥. To find this horizontal component, recall that we can use the formula 𝐴 subscript 𝑥 equals 𝐴 times cos 𝜃, where 𝐴 is the magnitude of the vector and 𝜃 is the argument of the vector.

We are told in the question that the magnitude of the vector 𝐀 is 55. We are also told that there is an angle of 82 degrees between the vector and the negative 𝑥-axis. But we need to be careful here; this angle is not the argument of the vector. The argument of a vector is defined as the angle between the vector and the positive 𝑥-axis, measured counterclockwise from the positive 𝑥-axis.

So, to find the argument of this vector, we need to add 180 degrees to this angle of 82 degrees. Adding 82 degrees plus 180 degrees gives us that the argument 𝜃 is equal to 262 degrees. Substituting these values for the magnitude 𝐴 and the argument 𝜃 into our equation, we find that the horizontal component 𝐴 subscript 𝑥 is equal to 55 multiplied by the cos of 262 degrees.

Completing this calculation, we find that the horizontal component 𝐴 subscript 𝑥 of the vector 𝐀 is equal to negative 7.654. We want this answer to the nearest whole number, so we can round down negative 7.654 to negative eight. And so we have arrived at the final answer. To the nearest whole number, the horizontal component of the vector 𝐀 is negative eight.

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