Question

Two vehicles start from the same point at the same time and move along line perpendicular to each other. Their speeds are $54km/hour$ and $72km/hour$ respectively. Find the rate at which the distance between them increases $20seconds$ after the start.

Answer 1

REF.Image

O is starting point for

2 cars,

$\Rightarrow$ They reach A & B

after 20 seconds

$OA=72\times \frac{5}{18}\times 20$

$=4\times 5\times 20=400$

$OB=54\times \frac{5}{18}\times 20$

$=3\times 5\times 20=300$

$\therefore AB=\sqrt{O{A}^2+O{B}^2}$

$=\sqrt{(400{)}^2+(300{)}^2}$

$=\sqrt{(16+9)(100{)}^2}=\sqrt{5^2\times (100{)}^2}$

$=5\times 100$

$\therefore AB=500$

$\therefore Rate=\frac{Distance}{Time}=\frac{500m}{20}$

$=25m/s$