1. ## relative velocity

at midday a ship P has position -11i+j km relative to lighthouse o. At the same time the position of boat Q is 4i-13j km relative to o. The velocities of P and Q are 3i km/h and xj km/h respectively.
if they are on a collision course what is the value of x

so i got their relative displacements which is -15i-14j
there relative velocities is 3i-xj
if i get the slope of both these they should be the same if they are on a collision course .
so -14/14=-x/3 x=2.8 the correct answer is 3. i do not see what I am doing wrong

2. ## Re: relative velocity

$x_p=-11+3t$

$y_p=1$

$x_q=4$

$y_q=-13+xt$

setting the position components equal ...

$-11+3t=4 \implies t=5$

$1=-13+x\cdot 5 \implies x = 2.8$

I agree with your solution. Maybe the given solution is rounded?

3. ## Re: relative velocity

yes the solution must be rounded.