Question

Two cars are moving. $A$ along east with $10m{s}^{-1}$. At any instant it is $1500m$ away from the crossing. $B$ at the same instant is $1800m$ away from the crossing and is moving towards the crossing along north direction with $15m{s}^{-1}$. When do they come closest?

• A. $109.3s$
• B. $129.2s$
• C. $119.3s$
• D. $99.3s$

Answer 1

Answer: (B)

$129.2s$

$x^2=(1500-10t{)}^2+(1800-15t{)}^2$, for $x$ to be minimum, its first derivative should be zero.
Thus, $\frac{dx}{dt}=0$
$=-20(1500-10t)-30(1800-15t)$
or $t=129.23s$