When Will Ships P & Q Be Closest to Each Other?

[dopey9]

A ship P is traveling due East at 30 km/h and a Ship Q is traveling due South at 40 km/h.
Both ships keep constant speed and course. At t=0 they are each 10 km from the point of intersection of their courses and moving towards the point.

Iv found the co-ordinates of Q relative to P at t=0
---->X=(10,10)km

iv also found the velocity of Q relative to P----> V= V[Q] -V[P]
-----.V= (0,40) - V(30,0)
----- V= (-30,40)km/h

but I am struggling to find the time at which P and Q are closest to each other...is there anyone that can help? thankz

 

[neutrino]

Find an expression for the distance between the ships as a function of time and minimise that with respect to time.

 

[Doc Al]

Iv found the co-ordinates of Q relative to P at t=0
---->X=(10,10)km

OK.

iv also found the velocity of Q relative to P----> V= V[Q] -V[P]
-----.V= (0,40) - V(30,0)
----- V= (-30,40)km/h

V[Q] = (0, -40)

but I am struggling to find the time at which P and Q are closest to each other

The trajectory of Q with respect to P is just a straight line. Write the equation of that line and then find the point on that line closest to point P. (There are several ways to do that.)

 

[dopey9]

can i just confirm that are these parts right that i answered before...because i wasnt too show whether a negitive sign is requied with the 10 coz of the direction?:
"Iv found the co-ordinates of Q relative to P at t=0
---->X=(10,10)km

iv also found the velocity of Q relative to P----> V= V[Q] -V[P]
-----.V= (0,40) - V(30,0)
----- V= (-30,40)km/h "

 

[Mindscrape]

Find an expression for the distance between the ships as a function of time and minimise that with respect to time.

Maybe I am misunderstanding your use of minimize, but there is no need for calculus here.

For the topic creator, you are pretty close and really just need to resolve your new vectors in a single linear equation. Then once you have your distance and velocity you know that a change in distance over a change in velocity is time.

 

[Doc Al]

"Iv found the co-ordinates of Q relative to P at t=0
---->X=(10,10)km

Right.

iv also found the velocity of Q relative to P----> V= V[Q] -V[P]
-----.V= (0,40) - V(30,0)
----- V= (-30,40)km/h "

Wrong. (As I pointed out earlier.)