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# Finding when a particle is traveling due east of it's origin, given vector equations. Watch

1. 7) A particle moves with a constant acceleration of (0.1i - 0.2j)ms^-2 . It is initially at the origin where it has velocity (-i+33j)ms^-1 . The unit vectors i and j are directed east and north respectively.

a) Find an expression for the position vector of the particle t seconds after it has left the origin. (2 marks)

b) Find the time that it takes for the particle to reach the point where it is due east of the origin. (3 marks)

So I got the first question to be s=(-i+3j)t+1/2(0.1i-0.2j)t^2. However I can't figure out how to do the second one, even by looking at the mark scheme (mm1b june 2012). Can anyone lend me a hand please :3 ?

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2. (Original post by progmaticOx)
7) A particle moves with a constant acceleration of (0.1i - 0.2j)ms^-2 . It is initially at the origin where it has velocity (-i+3j)ms^-1 . The unit vectors i and j are directed east and north respectively.

a) Find an expression for the position vector of the particle t seconds after it has left the origin. (2 marks)

b) Find the time that it takes for the particle to reach the point where it is due east of the origin. (3 marks)

So I got the first question to be s=(-i+3j)t+1/2(0.1i-0.2j)t^2. However I can't figure out how to do the second one, even by looking at the mark scheme (mm1b june 2012). Can anyone lend me a hand please :3 ?
you should rewrite your equation for the position vector - gather the i and j components together
eg.r = (i - j) + (2i + 3j)t

becomes r = (1 + 2t)i + (-1 + 3t)j
Then if something is due east (or west) note that the j component of displacement must be 0
-1 + 3t = 0
and solve for t

Do the same with your problem. You'll have a quadratic with 2 solutions, obviously one should be t=0 (when it is at the origin)
3. Thanks, I'll give this a go once I get back from my run.

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