Question

A ship A is moving Westwards with a speed
10 km h-1 and a ship B 100 km South of A
moving Northwards with a speed of 10 km h-1 The
time after which the distance between the
becomes shortest, is
[AIPMT-2015
(1) 10/2h
(2) Oh
(3) 5 h
(4) 52 h​

Answer 1

Explanation:

It is clear from the diagram that the shortest distance between the ship A and B is PQ.

Here, Sin45

0

=

OQ

PQ

⟹PQ=100×

2

1

=50

2

m

Also,

V

AB

=

V

A

2

+V

B

2

=

10

2

+10

2

=10

2

km/h

So, the time taken to reach shortest path is

t=

V

AB

PQ

=

10

2

50 2 =5h