How to Find Force F on a Boat with Given Forces and Motion?

[PandaBoy]

A 325-kg boat is sailing 15.0° north of east at a speed of 2.00 m/s. Thirty seconds later, it is
sailing 35.0° north of east at a speed of 4.00 m/s. During this time, three forces act on the boat:
a 31.0N force directed 15.0° north of east, a 23.0N force directed 15.0° south of west and F
Find the force F
Answer : [18.4N, 68.0° north of east]

Fr = F1 + F2 + F3 (due to 3 forces acting on it)

F3 = Fr - F1 - F2 (as question wanted to look for the 3rd force)

F1 = 31cos15° = 30.0N (to the right)

F2 = -(23cos15) = -22.2N (to the right. Or +ve to the left)

a = (v - u)/t

Do I need to search for the vertical, y and the horizontal, x component of the velocity to turn it into resultant Force? Through square root of (Fy^2 +Fx^2)? I do not understand the first 2 sentences of the question. So in the end they will turn into the resultant force acted on the boat? I am confused.

It is a relatively new topic in mechanics to me. I am sorry I could not even make a single line of solution.. >< i have no idea where to start calculating actually. Though I did forces of equilibrium before, this doesn't seems like anything from it.

 

[Doc Al]

Im not sure what to do with the velocity provided. Force doesn't involve velocity hmm..

But what about the change in velocity? What might that have to do with force?

 

[PandaBoy]

Oh so I would use the change in velocity to find the acceleration and thus make it into my resultant force? Hmm which means :

Uy = 2sin15° = 0.52m/s Vy = 4sin35° = 2.29m/s
Ux = 2cos15° = 1.93m.s Vx = 4cos35° = 3.28m/s

In which I have t=35s

Which means my a for x and y-component would be :

x : a = (3.28-1.93m/s)/35 = 0.04m/s^2
y : a = (2.29-0.52m/s)/35 = 0.05m/s^2

and from there I find my Fr which is

x : Fr = 13.0N
y : Fr = 16.3N

Then Fr = 20.8N?

Edit : Just tried solving it, I din get the amount as given by the answer. I am not sure where have I gone wrong.

 

[Doc Al]

In which I have t=35s

Recheck this value for time.

 

[PandaBoy]

Hey I got my answer! Thanks for the help Doc! I understood some part wrongly but I fixed my understanding now.
I think I should have no problem with the other questions now. Appreciate your real direct-to-the-point replies. Have a good day sir!