Question

A helicopter flies 11 miles south. It then turns 66 degrees east of south and travels an additional 42 miles. what is the direction of the helicopter resultant vector?

Answer 1

To determine the direction of the resultant vector for a helicopter that flies 11 miles south and then 42 miles at a 66-degree angle east of south, we use the components of the vectors along with trigonometric functions and the Pythagorean Theorem to calculate the total displacement and direction.

Step-by-step explanation:

The question asks about determining the direction of the resultant vector for a helicopter's journey, which involves vector addition. The helicopter flies 11 miles south and then turns 66 degrees east of south, flying an additional 42 miles. To find the direction of the resultant vector, we would typically use trigonometric methods, drawing the vectors and their components, and then apply the Pythagorean Theorem and inverse trigonometric functions to find the magnitude and direction.

We could liken this to a situation where we have two vectors: one representing the 11 miles south and the second representing the 42 miles at a 66-degree angle east of south. The components of these vectors along the north-south and east-west axes are found using sine and cosine functions, respectively. The total southward displacement is given by the sum of the south components of each vector, and the eastward displacement is given by the east component of the second vector since the first vector has no east component.

Once we have the components, we can calculate the resultant's magnitude using the Pythagorean Theorem (R = sqrt(S2 + E2)) and the direction using the inverse tangent function (tan-1(E/S)), where S and E are the south and east components respectively. The direction would be east of south, corresponding to the angle found from the inverse tangent calculation.

Answer 2

The direction of the helicopter resultant vector is 27.03 miles south of the west.

Step-by-step explanation:

To find the direction of the helicopter resultant vector, we need to add the two vectors together.

The first vector is 11 miles south, which we can represent as a vector of magnitude 11 in the negative y-direction.

The second vector is 42 miles in a direction 66 degrees east of south.

To find the components of this vector, we can use the sine and cosine functions.

The x-component is given by cos(66) * 42 = 21.16 miles.

Since it is south of the west, it is negative.

The y-component is given by sin(66) * 42 = 38.97 miles.

Since it is south, it is negative.

Adding the x-components and y-components, we get -21.16 miles west and -27.03 miles south.

Therefore, the direction of the helicopter resultant vector is 27.03 miles south of the west.