You walk 50 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?
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Correction:
X = 45*cos30 = 38.97.
Y = 50 + 45*sin30 = 72.5 m.
D^2 = (38.97)^2 + (72.5)^2 = 6774.91
D = 82.3 m.
To find out how far you are from where you originally started after walking 50 m to the north and then turning 60° to your right and walking another 45 m, you can use the concept of vectors and trigonometry.
Step 1: Visualize the scenario
Imagine you are standing at point A, and you walk 50 m to the north, ending up at point B. Then, you turn 60° to your right and walk 45 m, ending up at point C. You need to find the distance from point C to point A.
Step 2: Break down the motion into components
By considering the given information, we can break down the motion into two components:
- The north component (vertical): This component represents the distance you covered when you walked to the north.
- The east component (horizontal): This component represents the distance you covered when you turned right and walked in that direction.
Step 3: Calculate the north component
Since you walked 50 m to the north, the north component is equal to 50 m.
Step 4: Calculate the east component
To calculate the east component, we need to use trigonometry. We know that you turned 60° to the right and walked 45 m. This forms a right-angled triangle with the east component as the base, the north component as the height, and the hypotenuse as the total displacement.
Using trigonometry, we can find the east component using the cosine function:
cos(60°) = adjacent/hypotenuse
cos(60°) = east component/45
east component = 45 * cos(60°)
east component ≈ 22.5 m
Step 5: Calculate the displacement
Now that we have both the north and east components, we can calculate the displacement from point C to point A using the Pythagorean theorem.
displacement = √(north component^2 + east component^2)
displacement = √(50^2 + 22.5^2)
displacement ≈ √(2500 + 506.25)
displacement ≈ √(3006.25)
displacement ≈ 54.87 m
Therefore, you are approximately 54.87 m away from where you originally started.
X = 45*cos60 = 22.5 m.
Y = 50 + 45*sin60 = 89.0 m.
D = sqrt((22.5)^2+(89)^2) = 91.8 m.