# Thread: Show that S and B will collide...

1. ## Show that S and B will collide...

(In this question the unit vectors i and j are due east and north respectively.)

At noon a ship S is 600m due north of an observation point O and a speedboat B is 120m due north of the same point. The ship S has a constant velocity of $|7i+8j|ms^{-1}$ and the speedboat B has a constant velocity of $|7i+24j|ms^{-1}$.

b). Show that S and B will collide and find the time when this collision occurs and the position vector of the point of collision.

My attempt:

$600i + t(7i+8j) = 120i + t(7i+24j)$

From there I need to find what t equals. That would give me the time when they collide. I've tried rearranging the equation to get t on one side, I've even tried finding the magnitude of the component vectors, where 7i+24j would be 25, but I just can't work it out =\ . Please tell me how to work it out, and I will go from there.

2. Originally Posted by Viral
(In this question the unit vectors i and j are due east and north respectively.)

At noon a ship S is 600m due north of an observation point O and a speedboat B is 120m due north of the same point. The ship S has a constant velocity of $|7i+8j|ms^{-1}$ and the speedboat B has a constant velocity of $|7i+24j|ms^{-1}$.

b). Show that S and B will collide and find the time when this collision occurs and the position vector of the point of collision.

My attempt:

$600i + t(7i+8j) = 120i + t(7i+24j)$

From there I need to find what t equals. That would give me the time when they collide. I've tried rearranging the equation to get t on one side, I've even tried finding the magnitude of the component vectors, where 7i+24j would be 25, but I just can't work it out =\ . Please tell me how to work it out, and I will go from there.
position vector equation should be ...

600j + (7i+8j)t = 120j + (7i+24j)t

in the x-direction ...

7t = 7t (what does that say about their respective positions in the x-direction?)

in the y-direction ...

600+8t = 120+24t

solve for t.