Relative Motion: Solving for Time Elapsed for Boats A & B

[perdita_x]

Homework Statement

The raceboats A and B leave at the same time the beach at point O with zero initial velocity. The path of boat A forms an angle of 60º with the beach and the path of boat B forms an angle of 45º.
Both boats move with constant acceleration. Compute the time elapsed until the boats are a
distance d apart from each other.

Given are the acceleration of boat A & B, and the distance d.

Homework Equations

s = (1/2)at^2
a_B/A=a_B-a_A

The Attempt at a Solution

This question has really bothered me because I know its not very hard, but somehow I can't figure out how to start. I tried using the relative acceleration between the two boats in the formula, but that didnt give the right answer. If someone could just help me get started that would be great.

 

[Doc Al]

I tried using the relative acceleration between the two boats in the formula, but that didnt give the right answer.

There's nothing wrong with that approach. What did you get for the relative acceleration? (Be sure to treat the accelerations as vectors.)

 

[perdita_x]

There's nothing wrong with that approach. What did you get for the relative acceleration? (Be sure to treat the accelerations as vectors.)

We're always told that we should solve the problems symbolically first. So when I first tried, I just used it as in the formula with a_B/A=a_B-a_A to find B relative to A.

Im not exactly sure what you mean when you say I need to treat the accelerations as vectors. If you mean that I should split up each relative acceleration into x and y components, then say that a_B/A=sqrt(a_(B/A)x² + a_(B/A)y²), that doesn't give the correct answer either.

 

[Doc Al]

We're always told that we should solve the problems symbolically first. So when I first tried, I just used it as in the formula with a_B/A=a_B-a_A to find B relative to A.

OK, but that doesn't make use of the given angles. Do the accelerations have the same magnitude?

 

[perdita_x]

OK, but that doesn't make use of the given angles. Do the accelerations have the same magnitude?

Hm. Okay, they don't have the same magnitude. And I think I understand why I need to consider them as vectors.

So something along the lines of a_(B/A)x = a_Bcos45 - a_Acos60, the same in y direction, then find the magnitude of a_B/A and use that?

 

[Doc Al]

So something along the lines of a_(B/A)x = a_Bcos45 - a_Acos60, the same in y direction, then find the magnitude of a_B/A and use that?

Yes, that's the idea. (But be careful with signs.)

 

[perdita_x]

Thanks! And yes, must watch out for signs :D