M1 position vectors help
need help in part C .I AM REALLY STRUGGLING WITH IT.
Two cars A and B are moving on straight horizontal roads with constant velocities. The velocity of A is 20 m s1 due east, and the velocity of B is (10i +10j) , where i and j are unit vectors directed due east and due north respectively
. Initially, A is at the fixed origin O, and the position vector of B is 300i m relative to O. At time t seconds, the position vectors of A and B are r metres and s metres respectively.
(a) Find expressions for r and s in terms of t. (3)
(b) Hence write down an expression for AB in terms of t. (1)
(c) Find the time when the bearing of B from A is 045. (5)
(d) Find the time when the cars are again 300 m apart.
Two cars A and B are moving on straight horizontal roads with constant velocities. The velocity of A is 20 m s1 due east, and the velocity of B is (10i +10j) , where i and j are unit vectors directed due east and due north respectively
. Initially, A is at the fixed origin O, and the position vector of B is 300i m relative to O. At time t seconds, the position vectors of A and B are r metres and s metres respectively.
(a) Find expressions for r and s in terms of t. (3)
(b) Hence write down an expression for AB in terms of t. (1)
(c) Find the time when the bearing of B from A is 045. (5)
(d) Find the time when the cars are again 300 m apart.
Original post by ThomH97
What bearing is B moving from its starting point?
idk,in question they don't told us that
Original post by Qer
idk
Can you sketch a diagram of where A and B begin, and their velocities?
Original post by ThomH97
Can you sketch a diagram of where A and B begin, and their velocities?
Original post by Qer
So what direction is B travelling? And what's that as a bearing?
Original post by ThomH97
So what direction is B travelling? And what's that as a bearing?
45---north east
Original post by Qer
45---north east
Yup
So when will it be north east of car A? Or equivalently, when will car A be south west of it?
Original post by ThomH97
Yup
So when will it be north east of car A? Or equivalently, when will car A be south west of it?
So when will it be north east of car A? Or equivalently, when will car A be south west of it?
i don't understand this can you explain a bit more
Original post by Qer
i don't understand this can you explain a bit more
Looking at your diagram, B starts off due east of A, and A is going to be heading east. After a while, A will be due south (under) of B, but that's gone too far. At some point earlier, you'll have the 045 bearing. Can you see on your diagram when that will be? (Maybe trace A and B's movement with your fingers)
Original post by ThomH97
Yup
So when will it be north east of car A? Or equivalently, when will car A be south west of it?
So when will it be north east of car A? Or equivalently, when will car A be south west of it?
when the i component of B is equal to i component of A...
is that right?
Original post by Qer
when the i component of B is equal to i component of A...
is that right?
is that right?
That will be when B is due north of A. Can you see why that is?
Original post by Qer
tbh, I am very bad in this stuff and it dont know why it is ............
Can you type your answers to a and b?
If something is north east of something else, how many steps east (i direction) do you have to go if it is 5 steps north (j direction).
Original post by Qer
need help in part C .I AM REALLY STRUGGLING WITH IT.
Two cars A and B are moving on straight horizontal roads with constant velocities. The velocity of A is 20 m s1 due east, and the velocity of B is (10i +10j) , where i and j are unit vectors directed due east and due north respectively
. Initially, A is at the fixed origin O, and the position vector of B is 300i m relative to O. At time t seconds, the position vectors of A and B are r metres and s metres respectively.
(a) Find expressions for r and s in terms of t. (3)
(b) Hence write down an expression for AB in terms of t. (1)
(c) Find the time when the bearing of B from A is 045. (5)
(d) Find the time when the cars are again 300 m apart.
Two cars A and B are moving on straight horizontal roads with constant velocities. The velocity of A is 20 m s1 due east, and the velocity of B is (10i +10j) , where i and j are unit vectors directed due east and due north respectively
. Initially, A is at the fixed origin O, and the position vector of B is 300i m relative to O. At time t seconds, the position vectors of A and B are r metres and s metres respectively.
(a) Find expressions for r and s in terms of t. (3)
(b) Hence write down an expression for AB in terms of t. (1)
(c) Find the time when the bearing of B from A is 045. (5)
(d) Find the time when the cars are again 300 m apart.
Hi, sorry I forgot to respond before. Did you figure it out?
Also you can ask on my discord server I noticed that you joined but never spoke.
Original post by AspiringUnderdog
Hi, sorry I forgot to respond before. Did you figure it out?
Also you can ask on my discord server I noticed that you joined but never spoke.
Also you can ask on my discord server I noticed that you joined but never spoke.
still struggling can you explain please
Spoiler
(edited 5 years ago)
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