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Question

(C) Let the starting point be the origin $(0, 0)$.First displacement: $75 \, km$ North $\rightarrow \vec{d_1} = 75 \hat{j}$.Second displacement: $60 \

Vedclass · Accepted Answer

$132$

Vedclass · Answer

(C) Let the starting point be the origin $(0, 0)$.First displacement: $75 \, km$ North $\rightarrow \vec{d_1} = 75 \hat{j}$.Second displacement: $60 \, km$ North-east $\rightarrow \vec{d_2} = 60 \cos 45^{\circ} \hat{i} + 60 \sin 45^{\circ} \hat{j} = 30\sqrt{2} \hat{i} + 30\sqrt{2} \hat{j}$.Third displacement: $20 \, km$ East $\rightarrow \vec{d_3} = 20 \hat{i}$.The total displacement vector $\vec{R} = \vec{d_1} + \vec{d_2} + \vec{d_3} = (30\sqrt{2} + 20) \hat{i} + (75 + 30\sqrt{2}) \hat{j}$.Using $\sqrt{2} \approx 1.414$,$x = 30(1.414) + 20 = 42.42 + 20 = 62.42 \, km$.$y = 75 + 30(1.414) = 75 + 42.42 = 117.42 \, km$.The minimum distance (magnitude of displacement) is $S = \sqrt{x^2 + y^2} = \sqrt{(62.42)^2 + (117.42)^2} \approx \sqrt{3896 + 13787} = \sqrt{17683} \approx 132.97 \, km$.Rounding to the nearest integer,the distance is $132 \, km$.

Column-$I$	Column-$II$
$(1)$ Resultant of two vectors is maximum	$(a)$ $180^o$
$(2)$ Resultant of two vectors is minimum	$(b)$ $90^o$
	$(c)$ $0^o$

While travelling from one station to another,a car travels $75 \, km$ North,$60 \, km$ North-east,and $20 \, km$ East. The minimum distance between the two stations is.......$km$

Similar Questions

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Resultant of two vectors is maximum $(a)$ $180^o$

$(2)$ Resultant of two vectors is minimum $(b)$ $90^o$

$(c)$ $0^o$

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