Question

Find the y-component of this vector:

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42.2°
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101 m
Remember, angles are measured from the +x axis.
Y-component (m)

Answer 1

The y-component of a vector with a magnitude of 101 m and an angle of 42.2° from the positive x-axis is found using Vy = V · sin(θ). The approximate y-component is 67.56 m.

Step-by-step explanation:

To find the y-component of a vector given its magnitude and angle of direction, you use the sine function because angles in vector math are measured from the positive x-axis. In this question, we know the vector's magnitude is 101 m and it makes an angle of 42.2° with the positive x-axis. To calculate the y-component (Vy), we will use the following formula:

Vy = V · sin(θ)

Where V is the magnitude of the vector and θ is the angle made by the vector with the positive x-axis. Plugging in our values we get:

Vy = 101 m · sin(42.2°)

Using a calculator, find the sine of 42.2°:

sin(42.2°) ≈ 0.6691

Now multiply the magnitude of the vector by this sine value:

Vy = 101 m · 0.6691 ≈ 67.56 m

Therefore, the y-component of the vector is approximately 67.56 m.