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M1 vectors question

Hi,
7 A particle is initially at the point A, which has position vector 13.6i metres, withrespect to an origin O. At the point A, the particle has velocityð6i 2.4j ,and in its subsequent motion, it has a constant acceleration of 0:8i 0:1j . The unit vectors i and j are directed east and north respectively.
(a) Find an expression for the velocity of the particle t seconds after it leaves A.

(b) Find an expression for the position vector of the particle, with respect to theorigin O, t seconds after it leaves A.

(c) Find the distance of the particle from the origin O when it is travelling in anorth-westerly direction.

I can do a and b but with c I thought i would be negative and j would be positive so you form the v equation then make the i components negative but the mark scheme says its the j component.


Any advice??
Many thanks
Reply 1
Avatar for Zacken
Zacken
22
Original post by pygmypossum
...




This is the direction it's moving off in. This means that you have j component = -i component.

Or equivalent: i component = -j component. It's the same thing.

Solve that for tt.

So since v=(6−0.8t)i+(2.4+0.1t)j\mathbf{v} = (6-0.8t)i + (2.4 + 0.1t)j then 6−0.8t=−(2.4+0.1t)6-0.8t = -(2.4+ 0.1t) or 2.4+0.1t=−(6−0.8t)2.4 + 0.1t = -(6-0.8t) either is fine.
Reply 2
Avatar for pygmypossum
pygmypossum
OP
Original post by zacken


this is the direction it's moving off in. This means that you have j component = -i component.

Or equivalent: I component = -j component. It's the same thing.

Solve that for tt.

So since v=(6−0.8t)i+(2.4+0.1t)j\mathbf{v} = (6-0.8t)i + (2.4 + 0.1t)j then 6−0.8t=−(2.4+0.1t)6-0.8t = -(2.4+ 0.1t) or 2.4+0.1t=−(6−0.8t)2.4 + 0.1t = -(6-0.8t) either is fine.


thank you so much!!!
Reply 3
Avatar for pygmypossum
pygmypossum
OP
Original post by Zacken


This is the direction it's moving off in. This means that you have j component = -i component.

Or equivalent: i component = -j component. It's the same thing.

Solve that for tt.

So since v=(6−0.8t)i+(2.4+0.1t)j\mathbf{v} = (6-0.8t)i + (2.4 + 0.1t)j then 6−0.8t=−(2.4+0.1t)6-0.8t = -(2.4+ 0.1t) or 2.4+0.1t=−(6−0.8t)2.4 + 0.1t = -(6-0.8t) either is fine.


Thank you!
Reply 4
Avatar for Zacken
Zacken
22
Original post by pygmypossum
Thank you!


You're welcome!

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