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A vector has a magnitude of 20 units and makes an angle of 30 degrees with the horizontal. What is its vertical component?

Physics

ScanSolve AI Answer

Answer

C

Step-by-step solution

4 steps

  1. Identify the given values.

    The magnitude of the vector is V=20V = 20 units.
    The angle of inclination to the horizontal is θ=30∘\theta = 30^\circ.

  2. Apply the formula for the vertical component of a vector.

    The vertical component (VyV_y) is given by:

    Vy=Vsin⁡θV_y = V \sin \theta

  3. Substitute the values into the formula.

    Vy=20 units×sin⁡30∘V_y = 20 \text{ units} \times \sin 30^\circ

  4. Calculate the value.

    We know that sin⁡30∘=0.5\sin 30^\circ = 0.5.

    Vy=20 units×0.5V_y = 20 \text{ units} \times 0.5 Vy=10 unitsV_y = 10 \text{ units}

    The vertical component of the vector is 10 units.

    Comparing this with the given options:
    A. 10310\sqrt{3} units
    B. 17.32 units
    C. 10 units
    D. 20 units

    The correct option is C.

    The final answer is C. 10 units\boxed{\text{C. 10 units}}.

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