A road starts at a college and goes due north for 2000m. It then goes 2000m on a bearing 040 and end at a market.how far is the market from the college
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To find the distance between the college and the market, you can use the concepts of trigonometry and vector addition.
1. Start by breaking down the road into two components: the northward component and the eastward component.
The northward component is the initial 2000m that the road goes due north.
The eastward component can be calculated using trigonometry. Since the road goes on a bearing of 040° (measured from the north), this means it deviates 40° east from north. You can use trigonometry to find the eastward component using the formula: eastward component = magnitude * sin(angle). In this case, the magnitude is also 2000m.
2. Calculate the eastward component:
eastward component = 2000m * sin(40°) ≈ 1287.60m
3. Now, you can find the total displacement (or total distance) between the college and the market. The total displacement can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
total displacement = √(northward component^2 + eastward component^2)
= √(2000m^2 + 1287.60m^2)
≈ 2431.28m
Therefore, the market is approximately 2431.28 meters away from the college.