Jaggi starts walking towards North from a point ' S ' and after walking 15 m turns to his left and walks 10 m , again he walks 10 m turning to his left and finally walks 22 m turning to his left and reaches a point ' Q '. How far and in which direction is he from the point ' S '?

Correct option is D

1. Initial Position (S):Jaggi starts at $S$ and walks 15 m North.

   • New position: $(0,15)$ relative to $S(0,0)$.

2. Turn Left and Walk 10 m:Turning left from North means he now moves West.

   • New position: $(-10,15)$.

3. Turn Left Again and Walk 10 m:Turning left from West means he now moves South.

   • New position: $(-10,5)$.

4. Final Turn Left and Walk 22 m:Turning left from South means he now moves East.

   • New position: $(12,5)$.

Distance from Starting Point $S$:

Using the distance formula:

Distance=(x2−x1)2+(y2−y1)2\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}Distance=(x2​−x1​)2+(y2​−y1​)2​

Substituting:

Distance=(12−0)2+(5−0)2=122+52=144+25=169=13m\text{Distance} = \sqrt{(12 - 0)^2 + (5 - 0)^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \, \text{m}Distance=(12−0)2+(5−0)2​=122+52​=144+25​=169​=13m

Direction:

The final position is $(12,5)$. To find the direction relative to $S$:

Angle with East axis (tanθ)=Opposite side (y)Adjacent side (x)=512.\text{Angle with East axis (tan} \, \theta) = \frac{\text{Opposite side (y)}}{\text{Adjacent side (x)}} = \frac{5}{12}.Angle with East axis (tanθ)=Adjacent side (x)Opposite side (y)​=125​.

This indicates the direction is North-East.

Final Answer:

D) 13 m North-East