Question

A car is moving towards north with a speed of $5m/s$. A motorcyclist is moving towards east with the speed of $5m/s$. At time $t=0$, the motorcyclist is in due north of the car and is at a distance of $30m$ from the car. The time $t$ at which they will be closest to each other is

• A. $2s$
• B. $3s$
• C. $6s$
• D. $4s$

Answer 1

The correct option is B $3s$

We know that

${\overrightarrow{v}}_c=5\hat{j}$

${\overrightarrow{v}}_m=5\hat{i}$

What between $C$:

${\overrightarrow{r}}_{m/c}=30\hat{j}$

${\overrightarrow{r}}_{m/c}=0(\hat{i}+\hat{j})$

$\overrightarrow{r}={\overrightarrow{r}}_{M/C}+{\overrightarrow{v}}_{M/C}$

$=30\hat{j}+5(\hat{i}-\hat{j})$

$=5\hat{i}+(30-5)\hat{j}$

$|\overrightarrow{r}{|}^2={25}^2+5^2$

$=50t^2-300++900$

$t=3s$.

$\frac{d|\overrightarrow{r}{|}^2}{dt}=0+100t=300=0$