Two ships P and Q are moving along straight lines with constant velocities - Edexcel - A-Level Maths Mechanics - Question 4 - 2003 - Paper 1
Question 4
Two ships P and Q are moving along straight lines with constant velocities. Initially P is at a point O and the position vector of Q relative to O is (6i + 12j) km, ... show full transcript
Worked Solution & Example Answer:Two ships P and Q are moving along straight lines with constant velocities - Edexcel - A-Level Maths Mechanics - Question 4 - 2003 - Paper 1
Step 1
Find p and q in terms of t.
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Answer
The position vector of ship P at time t is given by:
p=10tj
The position vector of ship Q at time t is:
q=(6−8t)i+(12+6t)j
Step 2
Calculate the distance of Q from P when t = 3.
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Answer
To find the distance between P and Q, we calculate:
PQ=q−p=((6−8(3))i+(12+6(3))j)−(0i+10(3)j)
This results in:
PQ=(6−24)i+(12+18−30)j=−18i+0j
The distance is:
∣PQ∣=extDistance=sqrt(−18)2+02=18extkm
Step 3
Calculate the value of t when Q is due north of P.
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Answer
For Q to be due north of P, the x-component of q must equal zero:
