Two persons A and B are located in the X-Y pl | vedclass

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

Question

(A) Let at time $t$, the position of $A$ be $\overrightarrow{r}_A = (0 + 0t)\hat{i} + (0 + 2t)\hat{j} = 2t\hat{j}$.Let at time $t$, the position of $B

Vedclass · Accepted Answer

$2.5$ s

Vedclass · Answer

(A) Let at time $t$, the position of $A$ be $\overrightarrow{r}_A = (0 + 0t)\hat{i} + (0 + 2t)\hat{j} = 2t\hat{j}$.Let at time $t$, the position of $B$ be $\overrightarrow{r}_B = (0 + 2t)\hat{i} + (10 + 0t)\hat{j} = 2t\hat{i} + 10\hat{j}$.The relative position vector $\overrightarrow{r}_{AB} = \overrightarrow{r}_B - \overrightarrow{r}_A = 2t\hat{i} + (10 - 2t)\hat{j}$.The square of the distance $D^2 = |\overrightarrow{r}_{AB}|^2 = (2t)^2 + (10 - 2t)^2$.$D^2 = 4t^2 + 100 + 4t^2 - 40t = 8t^2 - 40t + 100$.For minimum distance, $\frac{d(D^2)}{dt} = 0$.$16t - 40 = 0$.$t = \frac{40}{16} = 2.5 	ext{ s}$.Since $\frac{d^2(D^2)}{dt^2} = 16 > 0$, the distance is minimum at $t = 2.5 	ext{ s}$.

Similar Questions

If the velocities of object $A$ and $B$ are $v_A$ and $v_B$ respectively,then write the equation of the relative velocity of $A$ with respect to $B$.

$A$ man crosses a $320 \ m$ wide river perpendicular to the current in $4 \ minutes$. If in still water he can swim with a speed $5/3$ times that of the current,then the speed of the current,in $m/min$ is

Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

$A$ boat is moving with a velocity of $3\hat i + 4\hat j$ in a river,and the water is moving with a velocity of $-3\hat i - 4\hat j$ with respect to the ground. The relative velocity of the boat with respect to the water is:

$A$ man is crossing a river flowing with a velocity of $5\, m/s$. He reaches a point directly across at a distance of $60\, m$ in $5\, s$. His velocity in still water should be ........ $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module