Two ships A and B are 10km apart on a line running south to north. Ship A farther north is streaming west at 20kmhr−1 and ship B is streaming north at 20kmhr−1. How long do they take to reach distance of closest approach?
A
10 minute
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
15 minute
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
20 minute
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
25 minute
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B 15 minute Ships A and B are moving with same speed 20kmhr−1 in the directions shown in figure. It is a two dimensional, two body problem with zero acceleration. Let us find →vBA.
Here, ∣∣→vBA∣∣=√(20)2+(20)2=20√2kmhr−1
i.e., →vBA is 20√2kmhr−1 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(1√2)km=5√2km
and the desired time is t=BC∣∣→vBA∣∣=5√220√2{BC=AC=5√2km}⇒t=14hr=15minutes