Question

A dog in an open field runs 11.0 m east and then 28.0 m in a direction 49.0 ∘ west of north. In what direction must the dog then run to end up 11.0 m south of her original starting point?

Answer 1

To find the direction the dog must run to end up 11.0 m south of her original starting point, we need to break down the dog's movements into vector components and find the resulting vector.

Step-by-step explanation:

To solve this problem, we need to break down the dog's movements into vector components. The dog initially runs 11.0 m east, so we can represent this as a vector with only an eastward component. Then, the dog runs 28.0 m in a direction 49.0° west of north. This can be broken down into northward and westward components using trigonometry.

Next, we need to find the vector that corresponds to being 11.0 m south of the starting point. This vector will have both a southward and a westward component.

To find the direction that the dog must run, we can sum up the eastward, northward, westward, and southward components. The resulting vector will point in the direction the dog needs to run.

In this case, the dog needs to run in a direction approximately 56.5° west of south to end up 11.0 m south of her original starting point.

Answer 2

`\theta=19.03 SE`

Explanation:

From the question we are told that:

`d_1=11.0m East`

`d_2=28.0m 49 \textdegree west\ north`

`d_3=10m south`

Generally the equation for Resolutions is mathematically given by

`d_x=-11-(-28sin49)`

`d_x=10.132m`

Where

`d_y=-11-(28cos49)`

`d_y=-29.37m`

Generally the equation for Direction is mathematically given by

`\theta=tan^(-1)((dx)/(dy))`

`\theta=tan^(-1)((10.132)/(29.37))`

`\theta=19.03 SE`