Question

A man at P observes a boat at a point B 1200
m from P in the direction of 047º. The boat
is moving due north of B at a speed of x
km/h. Fifteen minutes later, the boat reaches
a point C such that the bearing of C from P
is 030°. Find the value of x.​

Answer 1

Let the height of the balloon be h. So, initially, the distance between the man and the balloon is h/ root3 as shown in the figure. (This diagram is in the plane perpendicular to the ground.)

Next, when he has walked 400m in North direction, the balloon is over his head. The balloon travels in North-West direction, and the motion is eplained in the next diagram. (This is in a plane parallel to the ground.)

 

As it is clear, ABC is a right angled isosceles triangle, with AB = BC, as angle ACB is 45 degrees(North of West) and AB is perpendicular to BC(North and West).

So, we get,

h/root3 = 400,  

or, h =  m

Hence the ballon is at a height of   m (or 692.8 m)