Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    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.
    I got part a and part b, but i dont know how to start part c, can someone help me ?
    Offline

    10
    ReputationRep:
    Well you have an expression for the vector ab as a function of time yes? How could you use that in the context of this question
    Offline

    22
    ReputationRep:
    (Original post by alesha98)
    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.
    I got part a and part b, but i dont know how to start part c, can someone help me ?
    You've done part (b)

    So you know you can write AB = f(t)i + g(t)j - no?

    Now plug t = 3 (that's 3 hours after noon, so 15:00 hours) then you'll get AB = number * i + other number * j

    Now compute the length of this vector using sqrt(number^2 + other number^2)
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Zacken)
    You've done part (b)

    So you know you can write AB = f(t)i + g(t)j - no?

    Now plug t = 3 (that's 3 hours after noon, so 15:00 hours) then you'll get AB = number * i + other number * j

    Now compute the length of this vector using sqrt(number^2 + other number^2)
    ah thankyou. i thought i need to sub t = 1500 ... because there wasnt a colon between
    Offline

    22
    ReputationRep:
    (Original post by alesha98)
    ah thankyou. i thought i need to sub t = 1500 ... because there wasnt a colon between
    No problemo, glad I helped. They like referring to times without colons, you should get used to it. :-)
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.