Question

A man A moves in north direction with speed 1m/s and another man N moves in E-30°-N with 10m/s . Find the reletive velocity of A with respect to B.

Answer 1

man A moves in north direction with speed 1m/s

so we can write

$\vec v_a = 0 \hat i + 1 \hat j$

now for other person

another man B moves in E-30°-N with 10m/s

so we can write

$\vec v_b = 10cos30 \hat i + 10 sin30 \hat j$

$\vec v_b = 5\sqrt3 \hat i + 5 \hat j$

Now the reletive velocity of A with respect to B is given by

$v_{ab} = \vec v_a - \vec v_b$

$v_{ab} = (0 \hat i + 1 \hat j) - (5\sqrt3 \hat i + 5 \hat j)$

$v_{ab} = -5\sqrt3 \hat i - 4 \hat j$

magnitude is given by

$|v_{ab}| = \sqrt{(-5\sqrt3)^2 + (-4)^2}$

$|v_{ab}| = 9.54 m/s$

and its direction is

$\theta = tan^{-1}\frac{v_y}{v_x} = 204.8 degree$

so its S 24.8 W direction and magnitude is 9.54 m/s

Answer 2

Explanation:

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