## 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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## Comments on in this question i and j are unit vectors? »

## lolo a @ 10:55 am

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