Question

A ship is moving westwards with a speed of 10 kilometres per hour and 50 hundred kilometres south of a is moving north pole to the speed of 10 kilometres per hour the time after which the distance between them becomes shortest is​

Answer 1

Answer is attached

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Answer 2

Answer:

The time after which the distance between them becomes shortest is​ 250 hr.

Explanation:

Given that,

Velocity of ship $v_A= 10\ km/h$

Distance = 5000 km

Velocity of ship $v_B = 10\ km/h$

Let after time t hours distance between them

Ship A covered the distance is 10 t.

Ship B covered the distance is 10 t.

Ship B covered the distance from the origin

$d=5000-10t$

We need to calculate the time

$S_{t}=\sqrt{(10t)^2+(5000-10t)^2}$

On differentiating w.r.to t

$S'(t)=200t+20(5000-10t)(-10)$

For max/min

$S'{t}=0$

$200t+20(5000-10t)(-10)=0$

$400t-100000=0$

$t=\dfrac{100000}{400}$

$t=250\ hr$

Hence, The time after which the distance between them becomes shortest is​ 250 hr.