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A CAR TRAVELLS 6KM TOWARDS NORTH AN ANGLE OF 45 DEGREES TO THE EAST AND THEN TRAVELS DISTANCE OF 4 KM TOWARDS NORTH AT AN ANGLE OF 135 DEGREES TO THE EAST.HOW FAR IS THE POINT FROM THE STARTING POINT.WHAT ANGLE DOES THE STRAIGHT LINE JOINING IS INITIAL AND FINAL POSITION MAKES WITH THE EAST
Asked by pulagalarao.137 | 05 Jul, 2019, 18:06: PM
answered-by-expert Expert Answer
Let the car starts from O, origin of X-Y coordinate system.
It travels 6 km along the direction OA which is towards north and the line of travel makes 45° to East.
Then the car travels 4 km along AB towards north at an angle of 135° to East.
 
As shown in figure, coordinate of final position of the car ( √2 km, 5√2 km ).
 
Hence the displacement OB = begin mathsize 12px style square root of open parentheses square root of 2 close parentheses squared plus open parentheses 5 square root of 2 close parentheses squared end root space almost equal to space 7.2 space m end style
begin mathsize 12px style angle end styleBOA = tan-1(4/6) ≈ 34° . Initially OA makes an angle 45° to X-axis .
Hence OB makes an angle 79° to X-axis (East) .
Answered by Thiyagarajan K | 06 Jul, 2019, 22:15: PM

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