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3-2.Motion in Plane
hard
A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60 \,m$, then the magnitude of displacement would be$.....\,m$ (Given $\left.\cos 135^{\circ}=-0.7\right)$
A$42$
B$47$
C$19$
D$4$
(JEE MAIN-2022)
Solution
$d = R \theta$
$60= R \left(\frac{3 \pi}{4}\right)$
$R =\frac{60 \times 4}{3 \pi}=\frac{80}{\pi} m$
Displacement $=\sqrt{ R ^{2}+ R ^{2}-2 R ^{2} \cos 135}$
$\Rightarrow \sqrt{2 R ^{2}-2 R ^{2}(-0.7)}$
$\Rightarrow \sqrt{3.4 R ^{2}}=\sqrt{3.4\left(\frac{80}{\pi}\right)^{2}}$
$\approx 47\,m$
$60= R \left(\frac{3 \pi}{4}\right)$
$R =\frac{60 \times 4}{3 \pi}=\frac{80}{\pi} m$
Displacement $=\sqrt{ R ^{2}+ R ^{2}-2 R ^{2} \cos 135}$
$\Rightarrow \sqrt{2 R ^{2}-2 R ^{2}(-0.7)}$
$\Rightarrow \sqrt{3.4 R ^{2}}=\sqrt{3.4\left(\frac{80}{\pi}\right)^{2}}$
$\approx 47\,m$
Standard 11
Physics
