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# Mechanics questions Watch

1. A coastguard station O monitors the movements of ships in a channel. At noon, the station's radar records two ships moving with constant speed. Ship A is at the point with position vector (-3i+10j) km relative to O and has velocity (2i+2j) km/h. Ship B is at the point with position vector (6i+j) km and has velocity (-i+5j) km/h.

a) show that if the two ships maintain these velocities they will collide.

The coastguard radios ship A and orders it to reduce its speed to move with velocity (i+j) km/h. Given the A obeys this order and maintains this new constant velocity:

b) find an expression for the vector AB for time t hours after noon

c) find, to three significant figures, the distance between A and B at 1500 hours.

d) find the time at which B will be due north of A.
2. (Original post by Victoria Brown)
A coastguard station O monitors the movements of ships in a channel. At noon, the station's radar records two ships moving with constant speed. Ship A is at the point with position vector (-3i+10j) km relative to O and has velocity (2i+2j) km/h. Ship B is at the point with position vector (6i+j) km and has velocity (-i+5j) km/h.

a) show that if the two ships maintain these velocities they will collide.

The coastguard radios ship A and orders it to reduce its speed to move with velocity (i+j) km/h. Given the A obeys this order and maintains this new constant velocity:

b) find an expression for the vector AB for time t hours after noon

c) find, to three significant figures, the distance between A and B at 1500 hours.

d) find the time at which B will be due north of A.
Do you understand anything about vectors?
3. yh. Ive done part a. Im stuck on the rest of it.
4. (Original post by Victoria Brown)
yh. Ive done part a. Im stuck on the rest of it.
so the first thing to do is to write out vectors for A and for B, i.e. S= Xi+yj+t(ji+pj)

Once you have those vectors for A and B find the disttance between those two points.

Hope that helps, if you want I can write out how to do it or I can keep giving you hints
5. yh. Could you please write it out for me?
6. (Original post by Victoria Brown)
yh. Could you please write it out for me?
Sorry it took so long, and that my hand writing is less then average but here you go

That should give you the correct answer if I am not mistaken ask any questions you need to.
7. (Original post by Booyah)
Sorry it took so long, and that my hand writing is less then average but here you go

That should give you the correct answer if I am not mistaken ask any questions you need to.
Thanks

How would I do parts c and d?
8. (Original post by Victoria Brown)
Thanks

How would I do parts c and d?
C is relatively simple, sub in t=3 into the AB vector

D on the other hand requires for the i values to be equal so set the ivectors of S and S1 equal to each other.

Do you want me to write that as well? With a couple of diagrams explaining?
10. For c)

AB=(9-2t)i+(-9+4t)j Sub t=3

9-2(3)=3

-9+4(3) = 3

so AB = 3i+3j

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