Question 1
A vector in the xy plane has a magnitude of 25m and an x component of 12m. The angle it makes with the positive x axis is:
a.
64 degrees
b.
61 degrees
c.
26 degrees
d.
241 degrees
e.
29 degrees
25*Cos A = 12.
A =
the angle whose cosine is ... 12 / 25
To find the angle the vector makes with the positive x axis, we can use the inverse tangent function.
The formula to find this angle is given by:
angle = tan^(-1)(y component / x component)
In this case, the x component is 12m and the y component is not given. However, we can calculate it using the Pythagorean theorem since we know the magnitude of the vector.
Using the formula:
magnitude = sqrt((x component)^2 + (y component)^2)
25m = sqrt(12m)^2 + (y component)^2
25m = 144m + (y component)^2
(y component)^2 = 25m - 144m
(y component)^2 = -119m
Since we cannot take the square root of a negative number in this context, we can conclude that an error has occurred in the given information or calculation. The correct answer cannot be determined with the information provided.
To find the angle that the vector makes with the positive x-axis, we can use trigonometry. Specifically, we can use the inverse tangent function (arctan) to find the angle.
First, we need to find the y-component of the vector. We know that the magnitude of the vector is 25m and the x-component is 12m. We can use the Pythagorean theorem to find the y-component:
y = sqrt(magnitude^2 - x_component^2) = sqrt(25^2 - 12^2) = sqrt(625 - 144) = sqrt(481) ≈ 21.93m
Now, we have the x-component (12m) and the y-component (21.93m). We can use the arctan function to find the angle:
angle = arctan(y/x) = arctan(21.93/12) ≈ 61 degrees
So, the angle that the vector makes with the positive x-axis is approximately 61 degrees. Therefore, the answer is b. 61 degrees.