Relative Velocity Question

[abcde]

Could anyone give me the solution and the method for this question?
John was playing with a remote control plane which flew with constant speed. He wanted to fly the plane from A to B, 500 m due north. Due to a steady wind blowing due south, the plane was at C, which was 400 m from B after 25 seconds. Given that the wind was blowing at a speed of 6m/s, find the speed of the plane in still air.

 

[OakMoon!]

The plane has travelled 100m in 25 secons. So the speed of plane relative to wind is 100/25=4m/s
Vp/w=Vp-Vw.. since Velocity of wind is in opposite direction to the plane it is negative. 4-(-6)= 10m/s is the speed of plane in still air.

 

[abcde]

that was simple! thanks..

 

[abcde]

Here is another question.
At a particular instant, a pirate ship is on a bearing of 075 from a navy ship, 200 km away. The pirate ship is sailing on a course of 120(degrees) at a speed of 50 km/h while the navy ship is cruising due east at a speed of 80km/h. Find the velocity of the pirate ship relative to the navy ship. Given that the navy ship is equipped with a radar that can detect any pirate ship within a radius of 100km and that both ships do not change course, how long does it take before the pirate ship is detected by the navy ship? Correct your answer to the nearest minute.
I could do the first part but not th second part, the 'radar' one. How can one proceed in this type of question?

 

[abcde]

Moreover, when a question asks to give the velocity of A relative to B, is it sufficient to give the answer as for example -120i + 50j ? Or should the bearing of 292.6(degrees) be necessarily included as an answer to the question? Please reply quickly to both these posts.

 

[bluecapric]

Moreover, when a question asks to give the velocity of A relative to B, is it sufficient to give the answer as for example -120i + 50j ? Or should the bearing of 292.6(degrees) be necessarily included as an answer to the question? Please reply quickly to both these posts.

if they asked for VELOCITY, then bearing is required. velocity means speed with direction.

 

[abcde]

Come on intelligent people, answer my earlier post!