an archer is practising on a training course and moves a distance of 11m[E]of their original position, which was due south of the target. the archer is now [N28W]. how far is the archer from the target?
To determine the distance of the archer from the target, we need to use the Pythagorean theorem since we have two perpendicular sides of a right triangle (N and W).
First, let's split the displacement of the archer into its components:
Displacement along the N-S direction = 11m[E]
Displacement along the W-E direction = 0m, since the archer moved due South
Now, we can create a right triangle with the displacement as the two sides.
The western component of the displacement is N28W, which implies an angle of 28 degrees with the North direction. Since this angle is measured from the North, it forms a reference angle of 90 - 28 = 62 degrees with the positive x-axis (East).
Using trigonometry, we can determine the displacement along the W-E direction:
cos(62 degrees) = W / (Hypotenuse)
W = cos(62 degrees) * Hypotenuse
Since the displacement along the W-E direction is 0m, the Hypotenuse is equal to W.
Therefore:
W = cos(62 degrees) * W
W = 0.458 * W
0.542W = 0
This implies that W = 0.
Now, we can calculate the displacement along the N-S direction:
sin(62 degrees) = N / (Hypotenuse)
N = sin(62 degrees) * Hypotenuse
N = sin(62 degrees) * 11m[E]
N ≈ 9.9m[N]
Therefore, the archer is about 9.9 meters north of the target.
To find the distance between the archer's current position and the target, we can use the Pythagorean theorem.
First, let's break down the archer's movement into north and west components.
We know that the archer moved 11m to the east, which is perpendicular to the north-south axis. Therefore, the archer's north component remains the same, i.e., 28.
The archer's west component can be determined by subtracting the distance moved east from the original position. Since the original position was directly south of the target, the archer moved directly east, so the west component is 0.
Now, we have the north component (28) and the west component (0). Using these components, we can calculate the distance between the archer and the target using the Pythagorean theorem.
Distance = sqrt((north component)^2 + (west component)^2)
Distance = sqrt((28)^2 + (0)^2)
Distance = sqrt(784 + 0)
Distance = sqrt(784)
Distance ≈ 28 meters
Therefore, the archer is approximately 28 meters away from the target.
To find the distance between the archer's current position and the target, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we need to find the distance between the archer's current position ([N28W]) and the target. Let's break it down step by step:
1. Convert the direction to an angle: The direction N28W can be converted into an angle relative to the north direction. In this case, N28W means the angle between the north direction and a line 28 degrees west of north. So, the direction angle is 90 degrees (north) - 28 degrees (west) = 62 degrees.
2. Use trigonometry to find the distance: We know the distance moved by the archer is 11m east (which we can consider positive). Now, we can treat this as a right triangle, where the distance moved east is the horizontal leg, the distance from the archer to the target is the hypotenuse, and the vertical leg can be considered as zero since the archer didn't move north or south.
Using the cosine function, we can solve for the hypotenuse (distance to the target):
cos(angle) = adjacent/hypotenuse
cos(62 degrees) = 11m/hypotenuse
3. Rearrange the equation to solve for the hypotenuse:
hypotenuse = 11m / cos(62 degrees)
4. Calculate the hypotenuse distance:
hypotenuse ≈ 24.24m
Therefore, the archer is approximately 24.24 meters away from the target.