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

Two trains, each $30 \,m$ long, are travelling in opposite directions with velocities $5 \,m/s$ and $10 \,m/s$. They will cross each other after: (in $\,s$)

An observer moves with a constant speed along the line joining two stationary objects. He will observe that the two objects

$A$ train is moving towards the east and a car is moving towards the north,both with the same speed. The observed direction of the car to a passenger in the train is

Vedclass Test Series

Exam Paper Generator

Online Exam Module