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In this question the unit vectors i and j are due east and north respectively and position vectors are given with respect to a fixed origin O.
A ship S is moving with constant velocity (2i−3j) km h−1 and a ship R is moving with constant velocity 6i km h−1.
a Find the bearing along which S is moving.
At noon S is at the point with position vector 8i km and R is at O. At time t hours after noon, the position vectors of S and T are s km and r km respectively.
b Find s and r, in terms of t.
At time T hours, R is due north-east of S. Find
c the value of T,
d the distance between S and R at time T hours.
I need help with part c)
Answer to a) 56.3, b) s=8i+(2i−3j)t - r=6ti
For part c I'm confused; if R is due south east of S, would it not mean the i and j components would be the same? Well it's wrong and if I do go on to equate the i and j components then I get T = 2, which is incorrect - the right answer is T = 8.
Cheers
A ship S is moving with constant velocity (2i−3j) km h−1 and a ship R is moving with constant velocity 6i km h−1.
a Find the bearing along which S is moving.
At noon S is at the point with position vector 8i km and R is at O. At time t hours after noon, the position vectors of S and T are s km and r km respectively.
b Find s and r, in terms of t.
At time T hours, R is due north-east of S. Find
c the value of T,
d the distance between S and R at time T hours.
I need help with part c)
Answer to a) 56.3, b) s=8i+(2i−3j)t - r=6ti
For part c I'm confused; if R is due south east of S, would it not mean the i and j components would be the same? Well it's wrong and if I do go on to equate the i and j components then I get T = 2, which is incorrect - the right answer is T = 8.
Cheers