Question

(Example 3.21 Two ships A and B are 10 km apart on a li
farther north is streaming west at 20 km/h and ship B is stream
their distance of closest approach and how long do they take to
Part on a line running south to north. Ship
is streaming north at 20 km/h. What
ley take to reach it?​

Answer 1

fig. of the question

$\mathfrak{\huge{\red{\underline{\underline{Question:-}}}}}$

✒ Two ships A and B are 10 km apart on a line running south to north. Ship A farther north is streaming west at 20 km/h and ship B is streaming north at 20 km/h. What is their distance of closest approach and how long do they to reach it?

$\mathfrak{\huge{\green{\underline{\underline{Answer:-}}}}}$

=> 15 mins.

$\mathfrak{\huge{\blue{\underline{\underline{Solution:-}}}}}$

Ships A and B are moving with same speed 20 km/h in the directions shown in figure. It is two dimensional, two body problem with zero acceleration.

Let us find vBA

=> vBA = vB - vA

Here, |vBA| = √ (20)² + (20²) = 20√2 km/h

i.e.,

vBA is 20² km/h at an angle of 45° from east towards north.

Thus, the given problem can be simplified as:

A is at rest and B is moving with vBA in the direction shown in figure.

Therefore, the minimum distance between the two is

smin =AC=ABsin45°

$= > 10( \frac{1}{ \sqrt{2} } )km$

=> 5√2 km

And the desired time is:

$t = | \frac{ bc }{vba} | = | \frac{5 \sqrt{2} }{20 \sqrt{2} } | (bc = ac = 5 \sqrt{2} )km$

$= \frac{1}{4} hrs$

= 15 min

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