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A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east?
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Problem:
A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east?
Solution:
Step 1: Draw a diagram
Draw a diagram and label the points as shown below.
Step 2: Find the horizontal and vertical components of the two vectors
Horizontal component of the first vector = 6*cos(45^) = 6/√2
Vertical component of the first vector = 6*sin(45^) = 6/√2
Horizontal component of the second vector = 4*cos(135^) = -4/√2
Vertical component of the second vector = 4*sin(135^) = 4/√2
Step 3: Add the horizontal and vertical components of the two vectors
Horizontal component of the resultant vector = (6/√2) + (-4/√2) = 2/√2
Vertical component of the resultant vector = (6/√2) + (4/√2) = 10/√2
Step 4: Find the magnitude of the resultant vector
Magnitude of the resultant vector = √[(2/√2)^2 + (10/√2)^2] = √52 = 2√13 km
Step 5: Find the angle of the resultant vector with the east
Tanθ = (10/√2)/(2/√2) = 5
θ = tan^-1(5) = 78.69^
Step 6: Conclusion
The distance of the point from the starting point is 2√13 km and the angle of the straight line joining its initial and final positions with the east is 78.69^
A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east?
Solution:
Step 1: Draw a diagram
Draw a diagram and label the points as shown below.
Step 2: Find the horizontal and vertical components of the two vectors
Horizontal component of the first vector = 6*cos(45^) = 6/√2
Vertical component of the first vector = 6*sin(45^) = 6/√2
Horizontal component of the second vector = 4*cos(135^) = -4/√2
Vertical component of the second vector = 4*sin(135^) = 4/√2
Step 3: Add the horizontal and vertical components of the two vectors
Horizontal component of the resultant vector = (6/√2) + (-4/√2) = 2/√2
Vertical component of the resultant vector = (6/√2) + (4/√2) = 10/√2
Step 4: Find the magnitude of the resultant vector
Magnitude of the resultant vector = √[(2/√2)^2 + (10/√2)^2] = √52 = 2√13 km
Step 5: Find the angle of the resultant vector with the east
Tanθ = (10/√2)/(2/√2) = 5
θ = tan^-1(5) = 78.69^
Step 6: Conclusion
The distance of the point from the starting point is 2√13 km and the angle of the straight line joining its initial and final positions with the east is 78.69^
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A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east?
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A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car travels 6 km towards the north at an angle 45^ to the east and then travels distance of 4 km towards the north at an angle 135^ to the east. How far is the point from the starting point? What angle does the straight line joining its initial and final positions makes with the east?.
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