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29 April, 07:57

Vector has a magnitude of 4.40 m and is directed east. Vector has a magnitude of 3.40 m and is directed 39.0° west of north. What are (a) the magnitude and (b) the direction (counterclockwise from east) of? What are (c) the magnitude and (d) the direction (counterclockwise from east) of?

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  1. 29 April, 08:16
    0
    Magnitude = 4.056 m

    Direction = 42.3⁰

    Explanation:

    The vector is resolved in terms of the vertical and horizontal components. Let's look each of these separately.

    The vector 4.40 is directed East. This automatically becomes a horizontal component.

    But we know that there is a vector 3.40 North West. The angle the vector makes with the horizontal is 61⁰.

    Resolving the vectors should yield the horizontal and vertical components:

    Horizontal components

    The first component is 4.40 m

    The second one is derived by resolving 3.40 to the horizontal like this 3.40 * - cos 61⁰ = - 1.648 m

    Adding the horizontal component gives 4.40 m + (-1.648 m) = 2.752 m

    Vertical components

    Resolve 3.40 with the angle 61⁰ like this: vertical comp = 3.41 * sin 61

    = 2.98 m

    The magnitude is given by √[ (2.98) ² + (2.752) ²] = 4.056 m Ans

    The direction us given by tan⁻¹ (2.98/2.752) = 42.3⁰ Ans
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