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A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5?
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A car travel 6 km towards north at an angle of 45 degree to the east a...
Solution:
Step 1: Calculating the total displacement
- The car first travels 6 km at an angle of 45 degrees to the east.
- This can be broken down into two components: 6*cos(45) km towards east and 6*sin(45) km towards north.
- The eastward component is 6*cos(45) = 6*(√2/2) = 3√2 km.
- The northward component is 6*sin(45) = 6*(√2/2) = 3√2 km.
Step 2: Calculating the second displacement
- The car then travels 4 km at an angle of 135 degrees to the east.
- This can also be broken down into two components: 4*cos(135) km towards east and 4*sin(135) km towards north.
- The eastward component is 4*cos(135) = 4*(-√2/2) = -2√2 km.
- The northward component is 4*sin(135) = 4*(√2/2) = 2√2 km.
Step 3: Finding the final position
- To find the final position, we add up the eastward and northward components from both steps.
- Total eastward displacement = 3√2 - 2√2 = √2 km.
- Total northward displacement = 3√2 + 2√2 = 5√2 km.
Step 4: Calculating the distance from the starting point
- Using Pythagoras theorem, distance = √((√2)^2 + (5√2)^2) = √(2 + 50) = √52 km.
Step 5: Calculating the angle with east
- The angle with east can be found using the tangent inverse of the northward displacement divided by the eastward displacement.
- Angle = tan^(-1)(5√2 / √2) = tan^(-1)(5) = tan^(-1)(5).
Therefore, the distance from the starting point is √52 km and the angle with east is tan^(-1)(5). Hence, the correct answer is (B) √52 km, tan^(-1)(5).
Step 1: Calculating the total displacement
- The car first travels 6 km at an angle of 45 degrees to the east.
- This can be broken down into two components: 6*cos(45) km towards east and 6*sin(45) km towards north.
- The eastward component is 6*cos(45) = 6*(√2/2) = 3√2 km.
- The northward component is 6*sin(45) = 6*(√2/2) = 3√2 km.
Step 2: Calculating the second displacement
- The car then travels 4 km at an angle of 135 degrees to the east.
- This can also be broken down into two components: 4*cos(135) km towards east and 4*sin(135) km towards north.
- The eastward component is 4*cos(135) = 4*(-√2/2) = -2√2 km.
- The northward component is 4*sin(135) = 4*(√2/2) = 2√2 km.
Step 3: Finding the final position
- To find the final position, we add up the eastward and northward components from both steps.
- Total eastward displacement = 3√2 - 2√2 = √2 km.
- Total northward displacement = 3√2 + 2√2 = 5√2 km.
Step 4: Calculating the distance from the starting point
- Using Pythagoras theorem, distance = √((√2)^2 + (5√2)^2) = √(2 + 50) = √52 km.
Step 5: Calculating the angle with east
- The angle with east can be found using the tangent inverse of the northward displacement divided by the eastward displacement.
- Angle = tan^(-1)(5√2 / √2) = tan^(-1)(5) = tan^(-1)(5).
Therefore, the distance from the starting point is √52 km and the angle with east is tan^(-1)(5). Hence, the correct answer is (B) √52 km, tan^(-1)(5).
Community Answer
A car travel 6 km towards north at an angle of 45 degree to the east a...
(B)
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A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5?
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A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5? 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 travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5?.
A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5? 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 travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5?.
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A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5?, a detailed solution for A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5? has been provided alongside types of A car travel 6 km towards north at an angle of 45 degree to the east and then travels 4 km towards north at an angle of135 degree to the east .How far is the point from starting point ? What angle does the straight line joining it's initial and final position make with east? (A) root 50 km tan inverse 5 (B)root 52km tan inverse 5 (C)10 km tan inverse root 5? theory, EduRev gives you an
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