at t=0, let the 1st boat be at (0,0)
The 2nd boat is at (-c,c)
So, at time t, the 1st boat is at (0,6t)
and the 2nd boat is at (-c+5t,c)
The distance is thus
d^2 = (-c+5t)^2 + (c-6t)^2
= c^2 - 10ct + 25t^2 + c^2 - 12ct + 36t^2
= 2c^2 - 22ct + 51t^2
2d dd/dt = -22c + 102t
dd/dt = (51t-11c)/d
dd/dt=0 at t = 11c/51
So, plug that into the distance formula to get d. As you can see, the nearest distance depends on how far away the two boats were at first.
The first boat is sailing towards the North at the speed of 6 km per hour and sees that another boat is heading east at the speed of 5 km per hour. The second boat is to the northwest of the first boat. what is the minimum distance between two boats, assuming that they do not change their speed or course?
1 answer
1 answer