what are the components of a vector that has a magnitude of 1.5 m at the angle of 35 degrees with respect to the positive x axis

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X = hor = 1.5cos35 = 1.22m.

Y = ver. = 1.5sin35 = 0.86m.

To determine the components of a vector with a magnitude of 1.5 m at an angle of 35 degrees with respect to the positive x-axis, we can use trigonometric functions.

Let's consider the vector V with magnitude V = 1.5 m and angle θ = 35 degrees.

The x-component (Vx) of the vector can be found using the cosine function:

Vx = V * cos(θ)
Vx = 1.5 m * cos(35°)

Similarly, the y-component (Vy) of the vector can be found using the sine function:

Vy = V * sin(θ)
Vy = 1.5 m * sin(35°)

Calculating these values:

Vx = 1.5 m * cos(35°) ≈ 1.228 m
Vy = 1.5 m * sin(35°) ≈ 0.857 m

Therefore, the components of the vector with a magnitude of 1.5 m at an angle of 35 degrees with respect to the positive x-axis are approximately Vx ≈ 1.228 m and Vy ≈ 0.857 m.

To find the components of a vector that has a magnitude of 1.5 m at an angle of 35 degrees with respect to the positive x-axis, we can make use of trigonometric functions.

First, let's define the vector in terms of its components: V = (Vx, Vy).

We know that the magnitude of the vector, V, is given by the formula:

V = sqrt(Vx^2 + Vy^2)

In this case, the magnitude of the vector is given as 1.5 m. Substituting this value into the equation, we get:

1.5 = sqrt(Vx^2 + Vy^2)

Next, we can find the angle that the vector makes with the positive x-axis. This angle is given as 35 degrees.

We can use the trigonometric functions cosine (cos) and sine (sin) to relate the components of the vector to its magnitude and angle.

cos(θ) = Vx / V
sin(θ) = Vy / V

Here, θ refers to the angle between the vector and the positive x-axis.

Substituting the given values into these equations, we get:

cos(35 degrees) = Vx / 1.5
sin(35 degrees) = Vy / 1.5

Now we can solve for Vx and Vy. Rearranging the equations, we have:

Vx = cos(35 degrees) * 1.5
Vy = sin(35 degrees) * 1.5

Calculating these values using a scientific calculator or any trigonometric function evaluator, we find:

Vx ≈ 1.23 m
Vy ≈ 0.86 m

So, the components of the vector with a magnitude of 1.5 m at an angle of 35 degrees with respect to the positive x-axis are approximately Vx = 1.23 m and Vy = 0.86 m.