We appreciate your visit to A cross country runner runs due east for 6 km then changes course to E25 N and runs another 9 km To the nearest tenth. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The runner is approximately 8.98 km away from her starting point.
To find the distance of the runner from her starting point, we can use the concept of vector addition and trigonometry.
Let's break down the runner's movement into two components:
Eastward component: The runner initially runs due east for 6 km. Since this is in the eastward direction, the magnitude of this component is 6 km in the positive x-direction.
Northward component: After changing course to E25°N, the runner runs another 9 km. This can be broken down into two components: northward and eastward.
Using trigonometry, we can determine the magnitudes of these components:
The northward component is given by 9 km * sin(25°).
The eastward component is given by 9 km * cos(25°).
Now, let's calculate the magnitudes of the components:
Northward component = 9 km * sin(25°) ≈ 3.80 km
Eastward component = 9 km * cos(25°) ≈ 8.13 km
To find the total displacement from the starting point, we can add the magnitudes of the components using vector addition. This can be visualized as creating a right-angled triangle, with the eastward and northward components as the two sides.
Applying the Pythagorean theorem, the total displacement (d) is given by:
d = √((eastward component)^2 + (northward component)^2)
=[tex]\sqrt{(8.13 km)^2 + (3.80 km)^2}[/tex])
≈ [tex]\sqrt{(66.16 km^2 + 14.44 km^2}[/tex])
≈ [tex]\sqrt{80.6 km^2}[/tex]
≈ 8.98 km
Therefore, the runner is approximately 8.98 km away from her starting point.
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