Stage 2 Specialist Mathematics

Running head: STAGE 2 SPECIALIST MATHEMATICS
STAGE 2 SPECIALIST MATHEMATICS
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1STAGE 2 SPECIALIST MATHEMATICS
Introduction:
In this particular assignment the vector laws are used to represent the position and velocity of
two mosquitoes in space.
Part 1:
Let the initial position of the first mosquito is (a,b,c) = (1,2,3) and the velocity vector = [d,e,f]
= [2,4,3].
Also, let the initial position of the second mosquito is (g,h,l) = (4,5,6) and the velocity vector
= [m,n,p] = [1,3,4].
Hence, the position of the first mosquito at time t is
[1 + 2t, 2 + 4t, 3 + 3t]
And the position of second mosquito at time t is
[4 + t, 5 + 3t, 6 + 4t]
These are the parametric equations of position of mosquitos at time t where unit of position is
in cm.
The velocity of 1st mosquito is v1 = 2i + 4j + 3k
Hence, speed = ||v|| = √22+ 42+ 32 = 5.385.
Now, let the two positions along the straight line for first and second mosquito are [7, 14, 12]
and [8, 17, 22].
Hence, the time required to reach [7, 14, 12] for first mosquito is
t1 = (final x position – initial x position)/x-component of velocity vector = (7 – 1)/2 = 3
Now, the time required for 2nd mosquito to reach [8, 17, 22] is