The problem can be solved using vector addition and trigonometry.

Step 1: Break down each movement into its eastward and northward components.

For the first movement:
The car travels 6 km at an angle of 45° to the east. This can be broken down into:
- Eastward component: 6 km * cos(45°) = 4.24 km
- Northward component: 6 km * sin(45°) = 4.24 km

For the second movement:
The car travels 4 km at an angle of 135° to the east. This can be broken down into:
- Eastward component: 4 km * cos(135°) = -2.83 km (negative because it's westward)
- Northward component: 4 km * sin(135°) = 2.83 km

Step 2: Add up the components to find the total eastward and northward movement.

- Total eastward movement: 4.24 km - 2.83 km = 1.41 km
- Total northward movement: 4.24 km + 2.83 km = 7.07 km

Step 3: Use the Pythagorean theorem to find the total distance from the starting point.

Distance = sqrt((1.41 km)^2 + (7.07 km)^2) = 7.28 km

Step 4: Use trigonometry to find the angle the final position makes with the east.

Angle = atan(7.07 km / 1.41 km) = 78.69°

So, the car is 7.28 km from the starting point, and the line joining the initial and final positions makes an angle of 78.69° with the east.

Question

The problem can be solved using vector addition and trigonometry.

Step 1: Break down each movement into its eastward and northward components.

For the first movement:
The car travels 6 km at an angle of 45° to the east. This can be broken down into:
- Eastward component: 6 km * cos(45°) = 4.24 km
- Northward component: 6 km * sin(45°) = 4.24 km

For the second movement:
The car travels 4 km at an angle of 135° to the east. This can be broken down into:
- Eastward component: 4 km * cos(135°) = -2.83 km (negative because it's westward)
- Northward component: 4 km * sin(135°) = 2.83 km

Step 2: Add up the components to find the total eastward and northward movement.

- Total eastward movement: 4.24 km - 2.83 km = 1.41 km
- Total northward movement: 4.24 km + 2.83 km = 7.07 km

Step 3: Use the Pythagorean theorem to find the total distance from the starting point.

Distance = sqrt((1.41 km)^2 + (7.07 km)^2) = 7.28 km

Step 4: Use trigonometry to find the angle the final position makes with the east.

Angle = atan(7.07 km / 1.41 km) = 78.69°

So, the car is 7.28 km from the starting point, and the line joining the initial and final positions makes an angle of 78.69° with the east.

Knowee AI · Accepted Answer

The problem can be solved using vector addition and trigonometry.

Step 1: Break down each movement into its eastward and northward components.

For the first movement:
The car travels 6 km at an angle of 45° to the east. This can be broken down into:
- Eastward component: 6 km * cos(45°) = 4.24 km
- Northward component: 6 km * sin(45°) = 4.24 km

For the second movement:
The car travels 4 km at an angle of 135° to the east. This can be broken down into:
- Eastward component: 4 km * cos(135°) = -2.83 km (negative because it's westward)
- Northward component: 4 km * sin(135°) = 2.83 km

Step 2: Add up the components to find the total eastward and northward movement.

- Total eastward movement: 4.24 km - 2.83 km = 1.41 km
- Total northward movement: 4.24 km + 2.83 km = 7.07 km

Step 3: Use the Pythagorean theorem to find the total distance from the starting point.

Distance = sqrt((1.41 km)^2 + (7.07 km)^2) = 7.28 km

Step 4: Use trigonometry to find the angle the final position makes with the east.

Angle = atan(7.07 km / 1.41 km) = 78.69°

So, the car is 7.28 km from the starting point, and the line joining the initial and final positions makes an angle of 78.69° with the east.

A car travels 6 km towards north at an angle of 45°to the east and then travels distance of 4 kmtowards north at an angle of 135° to the east. Howfar is the point from the starting point? What angledoes the straight line joining its initial and finalposition makes with the east

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