Question

Mr. Khanna walked 40 meters towards East, took a right turn and walked 60 meters. Then he took a left turn and walked 40 meters. How far and in which direction is he now from the starting point?

• A. 80 meters, East
• B. 100 meters, South-East
• C. 80 meters, South-East
• D. 100 meters, South

Hint:

Remember that when dealing with distance in two directions (like East and South), the Pythagorean theorem can be used to calculate the resultant distance if the directions are perpendicular.

Answer 1

The Correct Option is B

Mr. Khanna's Walking Path Solution

Step 1: Mr. Khanna walks 40 meters towards East.

Step 2: He then takes a right turn and walks 60 meters South.

Step 3: He takes a left turn and walks 40 meters towards East.

Final Position:

Total movement in the East direction = \( 40 + 40 = 80 \) meters.

Total movement in the South direction = \( 60 \) meters.

Distance from the starting point:

Using the Pythagorean theorem:

\[ \text{Distance} = \sqrt{(80)^2 + (60)^2} \] \[ = \sqrt{6400 + 3600} \] \[ = \sqrt{10000} = 100 \text{ meters} \]

Direction:

The displacement forms a right-angled triangle where the direction is found using:

\[ \theta = \tan^{-1} \left(\frac{60}{80}\right) \] \[ = \tan^{-1} (0.75) \] \[ \approx 37^\circ \text{ South-East} \]

Final Answer:

100 meters, South-East.