A man travels 30 m along the direction of 3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The initial displacement vector $\vec{S}_1$ is along the direction of $3 \hat{i} + 4 \hat{j}$. The unit vector is $\hat{u} = \frac{3 \hat{i} + 4 \

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(D) The initial displacement vector $\vec{S}_1$ is along the direction of $3 \hat{i} + 4 \hat{j}$. The unit vector is $\hat{u} = \frac{3 \hat{i} + 4 \hat{j}}{\sqrt{3^2 + 4^2}} = \frac{3 \hat{i} + 4 \hat{j}}{5}$.Thus,$\vec{S}_1 = 30 	imes \left(\frac{3 \hat{i} + 4 \hat{j}}{5}ight) = 18 \hat{i} + 24 \hat{j} \ m$.Let the second displacement be $\vec{S}_2 = d \hat{n}$,where $\hat{n}$ is a unit vector perpendicular to $\vec{S}_1$. Since $\vec{S}_1 = 18 \hat{i} + 24 \hat{j}$,a perpendicular vector is proportional to $4 \hat{i} - 3 \hat{j}$.So,$\vec{S}_2 = k(4 \hat{i} - 3 \hat{j})$. The magnitude is $d = |k| \sqrt{4^2 + (-3)^2} = 5|k|$.The total displacement $\vec{S}_{net} = \vec{S}_1 + \vec{S}_2 = (18 + 4k) \hat{i} + (24 - 3k) \hat{j}$.Since the net displacement is along the $x$-axis,the $y$-component must be zero:$24 - 3k = 0 \implies k = 8$.Then $\vec{S}_2 = 8(4 \hat{i} - 3 \hat{j}) = 32 \hat{i} - 24 \hat{j}$.The magnitude $d = |\vec{S}_2| = \sqrt{32^2 + (-24)^2} = \sqrt{1024 + 576} = \sqrt{1600} = 40 \ m$.

Column-$I$	Column-$II$
$(1)$ Resultant of two mutually perpendicular vectors	$(a)$ Along the bisector of the angle between them
$(2)$ Direction of $\overrightarrow A \times \overrightarrow B$	$(b)$ Coplanar
	$(c)$ Perpendicular to the plane containing $\overrightarrow A$ and $\overrightarrow B$

Column $I$	Column $II$
$(A) \|A+B\|$	$(p) \frac{\sqrt{3}}{2} x^2$
$(B) \|A-B\|$	$(q) x$
$(C) A \cdot B$	$(r) \sqrt{3} x$
$(D) \|A \times B\|$	$(s) \frac{x^2}{2}$

$A$ man travels $30 \ m$ along the direction of $3 \hat{i} + 4 \hat{j}$ and then moves '$d$' meters perpendicular to the initial direction such that his total displacement is along the $x$-axis. What is the value of '$d$' in meters?

Similar Questions

$100$ coplanar forces,each equal to $10 \ N$,act on a body. Each force makes an angle of $\pi/50$ radians with the preceding force. What is the resultant of the forces in $N$?

Five equal forces of $10 \, N$ each are applied at one point and all are lying in one plane. If the angles between them are equal,the resultant force will be ........... $N$.

Two vectors $A$ and $B$ have equal magnitude $x$. The angle between them is $60^{\circ}$. Match the following two columns:

Column $I$ Column $II$

$(A) |A+B|$ $(p) \frac{\sqrt{3}}{2} x^2$

$(B) |A-B|$ $(q) x$

$(C) A \cdot B$ $(r) \sqrt{3} x$

$(D) |A \times B|$ $(s) \frac{x^2}{2}$

If $\overrightarrow{A}=3 \hat{\imath}-2 \hat{\jmath}+\hat{k}$,$\overrightarrow{B}=\hat{\imath}-3 \hat{\jmath}+5 \hat{k}$ and $\overrightarrow{C}=2 \hat{\imath}+\hat{\jmath}-4 \hat{k}$ form a right-angled triangle,then which of the following is satisfied?

Vedclass Test Series

Exam Paper Generator

Online Exam Module