A biker rides700m north 300m east 400m north, 100m west, 1200m south 300m east and finally 100m north .Draw the path of motion of the biker. What distance did he cover?What was his displacement?
To draw the path of motion of the biker, let's begin with a central point (0,0) and mark the movements step by step:
1. The biker rides 700m north, so from (0,0) go 700m straight up to (0,700).
2. The biker then goes 300m east, so from (0,700) move 300m to the right to (300,700).
3. Next, the biker rides 400m north, so from (300,700) go 400m straight up to (300,1100).
4. The biker goes 100m west, so from (300,1100) move 100m to the left to (200,1100).
5. Then, the biker rides 1200m south, so from (200,1100) go 1200m straight down to (200,-100).
6. The biker goes 300m east, so from (200,-100) move 300m to the right to (500,-100).
7. Finally, the biker rides 100m north, so from (500,-100) go 100m straight up to (500,0).
The path of motion of the biker can be represented as follows:
Starting point: (0,0)
Movement 1: (0,700)
Movement 2: (300,700)
Movement 3: (300,1100)
Movement 4: (200,1100)
Movement 5: (200,-100)
Movement 6: (500,-100)
Movement 7: (500,0)
The drawn path would resemble a zigzag pattern.
To calculate the distance covered by the biker, we sum up the lengths of each movement:
Distance covered = 700m + 300m + 400m + 100m + 1200m + 300m + 100m = 3100m
The displacement is the straight-line distance between the starting point and the final position, regardless of the actual path taken.
Using the Pythagorean theorem, we can calculate the displacement:
Displacement = √((500 - 0)^2 + (0 - 0)^2) = √(500^2) = 500m
Therefore, the biker covered a distance of 3100m and had a displacement of 500m.
To draw the path of motion of the biker, we can start with a reference point, such as the origin (0,0) on a coordinate plane. We can then plot each movement of the biker on the plane.
1. Start at the origin (0,0).
2. Move 700m north, so we move up on the y-axis to (0,700).
3. Move 300m east, so we move right on the x-axis from (0,700) to (300,700).
4. Move 400m north from (300,700), so we move up on the y-axis to (300,1100).
5. Move 100m west from (300,1100), so we move left on the x-axis to (200,1100).
6. Move 1200m south from (200,1100), so we move down on the y-axis to (200,-100).
7. Move 300m east from (200,-100), so we move right on the x-axis to (500,-100).
8. Finally, move 100m north from (500,-100), so we move up on the y-axis to (500,0).
The path of motion of the biker on the coordinate plane is as follows:
(0,0) -> (0,700) -> (300,700) -> (300,1100) -> (200,1100) -> (200,-100) -> (500,-100) -> (500,0).
To calculate the distance the biker covered, we can sum up the distances between consecutive points on the path. Using the distance formula, the total distance is:
Distance = √[(300-0)² + (700-0)²] + √[(300-300)² + (1100-700)²] + √[(200-300)² + (700-1100)²] + √[(200-200)² + (-100-700)²] + √[(500-200)² + (-100+100)²] + √[(500-500)² + (0+100)²]
= √(300² + 700²) + √(0² + 400²) + √((-100)² + 400²) + √(0² + 800²) + √(300²) + √100²
= √(90000 + 490000) + √(160000) + √(100000 + 160000) + √(640000) + 300 + 100
= √580000 + 400 + √260000 + √260000 + 560 + 300 + 100
≈ 761.94 + 400 + 509.9 + 509.9 + 560 + 300 + 100
≈ 3041.74m
Therefore, the biker covered a distance of approximately 3041.74 meters.
To calculate the displacement of the biker, we measure the straight-line distance from the initial point (0,0) to the final point (500,0). Using the distance formula, the displacement is:
Displacement = √[(500-0)² + (0-0)²]
= √(500² + 0²)
= √(250000)
= 500m
Therefore, the displacement of the biker is 500 meters.
so, did you draw the path?
where did you end up?
Hint: label the start (0,0)
Distance covered is just the sum of all the line segments.
Final displacement is found using the normal distance formula, which is just the Pythagorean Theorem.