1. ## collision

if boat x has position 2 i 7 j and velocity 4 i 5 j and boat y has position 6 i 9 j and velocity 3 i 4 j prove they are on a collision course .

im trying to do this by finding there relative positions and velocities. im trying to make use of if they are on a collision course their velocities in the direction perpendicular to them in the j direction must be equal

2. ## Re: collision

if boat x has position 2 i 7 j and velocity 4 i 5 j and boat y has position 6 i 9 j and velocity 3 i 4 j prove they are on a collision course .
do all the positions and velocities have strictly positive components? (I don't see any + or - signs)

3. ## Re: collision

Originally Posted by markosheehan
if boat x has position 2 i 7 j and velocity 4 i 5 j and boat y has position 6 i 9 j and velocity 3 i 4 j prove they are on a collision course .
So at any time, t, boat x has position vector <2, 7>+ t<4, 5>= <2+ 4t, 7+ 5t>.
And boat y has position vector <6, 9>+ t<3, 4>= <6+ 3t, 9+ 4t>. Is there any time, t, such that those two positions are the same? That is, is there one value of t such that 2+ 4t= 6+ 3t and 7+ 5t= 9+ 4t? It should be easy to solve the first equation for t, then substitute that value of t to check if it also satisfies the second equation.

im trying to do this by finding there relative positions and velocities. im trying to make use of if they are on a collision course their velocities in the direction perpendicular to them in the j direction must be equal
In "their velocities in the direction perpendicular to them", what does "them" refer to?

4. ## Re: collision

Sorry ye all their velocities and displacements are positive. Ye I know how to solve for the time when they collide but is there a way just to prove they will collide

5. ## Re: collision

Originally Posted by markosheehan
Sorry ye all their velocities and displacements are positive. Ye I know how to solve for the time when they collide but is there a way just to prove they will collide
not really. The courses could cross without collision. You have to ensure that the positional intersection of the courses occurs at the same time for a collision to occur so one way or the other you're going to need that time.

6. ## Re: collision

Originally Posted by markosheehan
Sorry ye all their velocities and displacements are positive. Ye I know how to solve for the time when they collide but is there a way just to prove they will collide
You say "I know how to solve for the time when they collide". So do that! If there is such a time then they will collide!