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Ravi is walking in the East direction. After walking a distance of 1 kilometer, he turns 45º left, and then 90º right. In which direction is he now?
- a)North
- b)West
- c)North-West
- d)South- East
Correct answer is option 'D'. Can you explain this answer?
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Ravi is walking in the East direction. After walking a distance of 1 k...
Degrees to his right and continues walking. After walking another 1 kilometer, he turns 60 degrees to his left and continues walking. How far and in what direction is Ravi from his starting point?
To solve this problem, we can use vector addition. Let's break down Ravi's movements into vectors.
When Ravi walks 1 kilometer in the East direction, we can represent this as a vector: E = 1 km East.
When Ravi turns 45 degrees to his right, we need to find the vector representing this turn. Since he turned right, the vector will be perpendicular to the East direction. Let's call this vector R. R will be pointing towards the South-East direction. To find the magnitude of R, we can use the trigonometric relationship sine(45) = opposite/hypotenuse, where the hypotenuse is 1 km (the distance Ravi walked) and the opposite side is the magnitude of R. Solving for the magnitude of R, we get R = 1 * sin(45) km = √2/2 km. The direction of R will be 45 degrees to the South of East.
When Ravi walks another 1 kilometer after turning, we can represent this as a vector: F = 1 km South-East.
When Ravi turns 60 degrees to his left, we need to find the vector representing this turn. Since he turned left, the vector will be perpendicular to the F vector. Let's call this vector L. L will be pointing towards the North-East direction. To find the magnitude of L, we can use the trigonometric relationship sine(60) = opposite/hypotenuse, where the hypotenuse is 1 km (the distance Ravi walked) and the opposite side is the magnitude of L. Solving for the magnitude of L, we get L = 1 * sin(60) km = √3/2 km. The direction of L will be 60 degrees to the North of East.
Now, let's add up all the vectors to find Ravi's final position. Adding E, R, and F:
E + R + F = 1 km East + (√2/2) km South-East + 1 km South-East.
Since the South-East vectors cancel out, we have:
E + R + F = 1 km East + (√2/2) km South-East + 1 km South-East
= 1 km East + (√2/2 + 1) km South-East.
So, Ravi is √2/2 + 1 kilometers away from his starting point, in the South-East direction.
To solve this problem, we can use vector addition. Let's break down Ravi's movements into vectors.
When Ravi walks 1 kilometer in the East direction, we can represent this as a vector: E = 1 km East.
When Ravi turns 45 degrees to his right, we need to find the vector representing this turn. Since he turned right, the vector will be perpendicular to the East direction. Let's call this vector R. R will be pointing towards the South-East direction. To find the magnitude of R, we can use the trigonometric relationship sine(45) = opposite/hypotenuse, where the hypotenuse is 1 km (the distance Ravi walked) and the opposite side is the magnitude of R. Solving for the magnitude of R, we get R = 1 * sin(45) km = √2/2 km. The direction of R will be 45 degrees to the South of East.
When Ravi walks another 1 kilometer after turning, we can represent this as a vector: F = 1 km South-East.
When Ravi turns 60 degrees to his left, we need to find the vector representing this turn. Since he turned left, the vector will be perpendicular to the F vector. Let's call this vector L. L will be pointing towards the North-East direction. To find the magnitude of L, we can use the trigonometric relationship sine(60) = opposite/hypotenuse, where the hypotenuse is 1 km (the distance Ravi walked) and the opposite side is the magnitude of L. Solving for the magnitude of L, we get L = 1 * sin(60) km = √3/2 km. The direction of L will be 60 degrees to the North of East.
Now, let's add up all the vectors to find Ravi's final position. Adding E, R, and F:
E + R + F = 1 km East + (√2/2) km South-East + 1 km South-East.
Since the South-East vectors cancel out, we have:
E + R + F = 1 km East + (√2/2) km South-East + 1 km South-East
= 1 km East + (√2/2 + 1) km South-East.
So, Ravi is √2/2 + 1 kilometers away from his starting point, in the South-East direction.
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Ravi is walking in the East direction. After walking a distance of 1 kilometer, he turns 45º left, and then 90º right. In which direction is he now?a)Northb)Westc)North-Westd)South- EastCorrect answer is option 'D'. Can you explain this answer?
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