December 17, 2009
in this question i and j are unit vectors?
mba asked:
at 2pm the position vector relative to a lighthouse of ship A is (3i+j)km and its velocity is (-i+5j)kmh-1.at the same time ship B has position vector (-i+4j)km relative to the white house and velocity (2i+3j)kmh-1.Find ,after t hrs.
a)the position vector of A relative to the lighthouse.
b)the position vector of B relative to the lighthouse.
c)the position vector of A relative to B.
d)Find the time when A is due north of B.
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at 2pm the position vector relative to a lighthouse of ship A is (3i+j)km and its velocity is (-i+5j)kmh-1.at the same time ship B has position vector (-i+4j)km relative to the white house and velocity (2i+3j)kmh-1.Find ,after t hrs.
a)the position vector of A relative to the lighthouse.
b)the position vector of B relative to the lighthouse.
c)the position vector of A relative to B.
d)Find the time when A is due north of B.
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Comments on in this question i and j are unit vectors? »
a)(3 -t)i + (1 +5t)j
since position vector = initial position + velocity x t (time)
b)( -1 + 2t)i + (4 + 3t)j
c)position vector of B - position vector of A
(-1 + 2t -3 + t)i + (4 + 3t - 1 - 5t)j
(3t - 4)i + (3 - 2t)j
d) due north to B, so the i components are equal
therefore, 3 - t = 2t - 1
3t = 4
t = 4/3 hours = 1 hour 20 minutes