A boat B is moving westwards with a speed of 20 kmh -1 and a boat C 200 km south of B is moving norhtwards with a speed of 20 kmh -1. The time after which the distance between then becomes shortest is

Question

A boat B is moving westwards with a speed of 20 kmh -1 and a boat C 200 km south of B is moving norhtwards with a speed of 20 kmh -1. The time after which the distance between then becomes shortest is (A) 5 h (B) 5 / √2 h (C) 5 √2 h (D) 0 h

Tardigrade Admin · Accepted Answer

vecVC B=20 hatj+20 hati=20 √2 km Time taken to reach shortest distance between bande =(200 cos 45°/20 √2)=(100 √2/20 √2)=5 h

Q. A boat $B$ is moving westwards with a speed of $20 km h^{- 1}$ and a boat $C 200 km$ south of $B$ is moving norhtwards with a speed of $20 km h^{- 1}$ . The time after which the distance between then becomes shortest is

$5 h$

$5/ 2 h$

$52 h$

$0 h$

$V_{CB} = 20 \hat{j} + 20 \hat{i} = 202 km$
Time taken to reach shortest distance between bande
$= \frac{200 c o s 4 5 ^{\circ}}{20 2} = \frac{100 2}{20 2} = 5 h$

Q. A boat B is moving westwards with a speed of 20kmh−1 and a boat C200km south of B is moving norhtwards with a speed of 20kmh−1. The time after which the distance between then becomes shortest is

5h

5/2​h

52​h

0h