A student walk 50m on a bearing 025° and then 200m due east. How far is she from hr starting point
To find out how far the student is from her starting point, we can use the property that the distance and direction traveled can be represented as a vector.
First, let's determine the components of the vectors. The student walks 50m on a bearing of 025°, which means she travels 50m in the northeast direction. We can calculate the horizontal and vertical components using trigonometry.
The horizontal component is given by:
cos(25°) × 50m = 0.9063 × 50m = 45.31m (rounded to two decimal places)
The vertical component is given by:
sin(25°) × 50m = 0.4226 × 50m = 21.13m (rounded to two decimal places)
Now, the student walks 200m due east. This means she only travels in the horizontal direction, so the horizontal component of this vector is 200m and the vertical component is 0.
To find the total displacement, we add the horizontal and vertical components of each vector:
Horizontal component: 45.31m + 200m = 245.31m (rounded to two decimal places)
Vertical component: 21.13m + 0 = 21.13m (rounded to two decimal places)
Now we can find the distance using the Pythagorean theorem:
Distance = √(245.31m^2 + 21.13m^2) = √(60389.2561m^2 + 446.1769m^2) = √60835.433m^2 = 246.69m (rounded to two decimal places)
Therefore, the student is approximately 246.69 meters away from her starting point.