Question

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Question ⬇⬇
A ship is moving westwards with the speed of 10km/hr and a ship B 100km South of A, is moving Northwards with the speed of 10km/hr. The time after which the distance between them becomes shortest, is :-
a) 5 hr
b)5√2 hr
c)10√2 hr
d)0hr​

Answer 1

Answer:

The answer is 5 hours

Explanation:

Initially the distance between the two ships is 100 and ship B is to the South of Ship A, Consider the Position of Ship B as the origin at this point

After a time "t" hrs the ship A covers 10t km westward while ship B covers 10t km northwards

Therefore the distance between them is

d=√((-10t-0)^2+(100-10t)^2)

d=√(100t^2+10000-2000t+100t^2)

Differentiate wrt t we get

1/(2√(100t^2+10000-2000t+100t^2))*(200t-2000+200t)

For Maxima and minima equate above equation to 0

we get

400t-2000=0

t=5

Hence the distance will be shortest after 5 hours

Answer 2

Answer:

d) 0hr

when ship b moves 100 km towards A then it will be shortest distance between them and time taken by it to reach there will be 10/100=0.1hr or 6min