A person walks 25.0 North of East for 3.80 km. How far would the person walk due North and due East to the same location?
sin 25 = north direction/3.8
cos 25 = east direction/3.8
I don't understand??? how do you solve the answer in km. Do you do "(sign of 25)<in calc> multiplied by(3.8km)"?????
To find out how far the person would walk due North and due East to the same location, we can use trigonometry. Let's break down the problem step by step:
1. Establish the initial direction: The person is walking 25.0 North of East. This means they are deviating from the East direction by 25.0 degrees, while still heading primarily towards the North. So, their initial direction can be represented as N25°E.
2. Calculate the distance walked North: The person has walked 3.80 km in their initial direction. To determine the distance walked due North, we need to find the North component of the total displacement. We can use trigonometry to do this.
- To calculate the North component, we can use the sine function: sin(25°) = North component / 3.80 km.
- Rearranging the equation gives us: North component = 3.80 km * sin(25°).
- Plugging in the values and calculating gives us: North component = 1.623 km (rounded to three decimal places).
3. Calculate the distance walked East: Similarly, we can find the East component of the displacement using the cosine function.
- To calculate the East component, we use the cosine function: cos(25°) = East component / 3.80 km.
- Rearranging the equation gives us: East component = 3.80 km * cos(25°).
- Plugging in the values and calculating gives us: East component = 3.447 km (rounded to three decimal places).
4. Determine the distances walked due North and due East: We have found that the person walked 1.623 km due North and 3.447 km due East to reach the same location.
Therefore, to reach the same location, the person would need to walk approximately 1.623 km due North and 3.447 km due East.