A man travels 7.0km due north , then 10.0km east. Find the resultant displacement.
If he travels 7.0km 30degrees East of North,then 10.0km east, find the resultant displacement.
draw a triangle. the two sides of to right angle are 10km and 7km. find the hypotenuse
for the second one, break the vectors into North and East components, add them up to get the final location, then again use the distance formula.
To find the resultant displacement of the man's travel, we can use the Pythagorean theorem and trigonometric functions.
For the first scenario:
1. The man travels 7.0 km due north.
2. Then, he travels 10.0 km east.
We can represent the north direction as the positive y-axis and the east direction as the positive x-axis on a Cartesian coordinate system.
Using the Pythagorean theorem, the resultant displacement (R) can be calculated as follows:
R = √((7.0 km)^2 + (10.0 km)^2)
R = √(49.0 km^2 + 100.0 km^2)
R = √149.0 km^2
R ≈ 12.18 km
Therefore, the resultant displacement is approximately 12.18 km.
For the second scenario:
1. The man travels 7.0 km at an angle of 30 degrees east of north.
2. Then, he travels 10.0 km east.
To find the resultant displacement, we need to find the north and east components of the second leg of the journey.
North component = 7.0 km * sin(30°)
North component = 3.5 km
East component = 7.0 km * cos(30°) + 10.0 km
East component ≈ 6.06 km + 10.0 km
East component ≈ 16.06 km
Using the Pythagorean theorem, the resultant displacement (R) can be calculated as follows:
R = √((3.5 km)^2 + (16.06 km)^2)
R = √(12.25 km^2 + 257.7636 km^2)
R = √269.0136 km^2
R ≈ 16.4 km
Therefore, the resultant displacement is approximately 16.4 km.
To find the resultant displacement, you can use the Pythagorean theorem and trigonometry.
1) In the first scenario where the man travels 7.0km due north, then 10.0km east:
- Draw a vector to represent the North direction with a length of 7.0km.
- Draw a vector to represent the East direction with a length of 10.0km.
- Draw a line to connect the starting point to the ending point of the two vectors. This represents the resultant displacement.
- Use the Pythagorean theorem to find the length of the line (resultant displacement).
- The formula is: resultant displacement = sqrt((7.0km)^2 + (10.0km)^2)
- Calculate the resultant displacement using the formula: sqrt(49km^2 + 100km^2) = sqrt(149km^2) ≈ 12.206km
2) In the second scenario where the man travels 7.0km 30 degrees East of North, then 10.0km east:
- Draw a vector to represent the 7.0km 30 degrees East of North direction.
- Use trigonometry to split this vector into its North and East components.
- The North component (y-direction) is obtained by multiplying the magnitude (7.0km) by the sine of the angle (30 degrees): 7.0km * sin(30 degrees) ≈ 3.5km.
- The East component (x-direction) is obtained by multiplying the magnitude (7.0km) by the cosine of the angle (30 degrees): 7.0km * cos(30 degrees) ≈ 6.062km.
- Draw a vector to represent the East direction with a length of 10.0km, starting from the end point of the previous vector.
- Draw a line to connect the starting point to the ending point of the two vectors. This represents the resultant displacement.
- Use the Pythagorean theorem to find the length of the line (resultant displacement).
- The formula is: resultant displacement = sqrt((6.062km + 10.0km)^2 + (3.5km)^2)
- Calculate the resultant displacement using the formula: sqrt(16.062km^2 + 12.25km^2) = sqrt(28.312km^2) ≈ 5.319km
Therefore, the resultant displacement in the first scenario is approximately 12.206km, and in the second scenario is approximately 5.319km.