Question

6. A man walked 3 km towards East, then
5 km towards North-East, then 8 km
towards South and finally 5 km towards
Nath-East direction. The distance of his
present location from the starting point​

Answer 1

Answer:

North East

Step-by-step explanation:

Best of luck for your paper

Answer 2

The distance of his  present location from the starting point​ is 1.0114 km.

Step-by-step explanation:

1. Taking

   East  $\mathbf{=+\hat{i}}$

   West $\mathbf{=-\hat{i}}$

   North $\mathbf{=+\hat{j}}$

   South $\mathbf{=-\hat{j}}$

2. First cover displacement $\mathbf{\vec{L_{1}}=+3\hat{i}}$

   Second cover displacement $\mathbf{\vec{L_{2}}=+5\cos 45 \ \hat{i}+5\sin 45 \ \hat{j}}$

   Third cover displacement $\mathbf{\vec{L_{3}}=-8\hat{j}}$

   Fourth cover displacement $\mathbf{\vec{L_{4}}=+5\cos 45 \ \hat{i}+5\sin 45 \ \hat{j}}$

3. Total displacement $\mathbf{\vec{L}=\vec{L_{1}}+\vec{L_{2}}+\vec{L_{3}}+\vec{L_{4}}}$

   Total displacement                                  $\mathbf{(\vec{L})=+3\hat{i}+5\cos 45 \ \hat{i}+5\sin 45 \ \hat{j}-8\hat{j}+5\cos 45 \ \hat{i}+5\sin 45 \ \hat{j}}$

    $\mathbf{(\vec{L})=(+3+2\times 5\cos 45)\hat{i}+(-8+2\times 5\sin 45)\hat{j}}$     ...1)

4. Now

   Total distance $\mathbf{(L)=\sqrt{(+3+2\times 5\cos 45)^{2}+(-8+2\times 5\sin 45)^{2}}}$

   After solving above equation

  Total distance (L) = 10.114 km