Thank you! I did Jan 09 a while back, I'll redo that paper and do the 2001/2 ones as well(Original post by areebmazhar)
In june 2002, june 2001 and jan 09 you could lose 13 or 14 marks and still get full ums, so it indicates that these paers had some very hard questions in Normally you need full marks to get full ums!
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(Original post by Jukeboxing)
Distance
Btw, could you please reply to my post: http://www.thestudentroom.co.uk/show...&postcount=309
thanks. 
(Original post by emma3)
Is the answer for d) 4.25 ? If it is, I'll explain how I did it, if not  I'll have to rethink, haha 
(Original post by arnab)
Any help with this question?
At time t = 0, a football player kicks a ball from the point A with position vector (2i + j) m
on a horizontal football field. The motion of the ball is modelled as that of a particle
moving horizontally with constant velocity (5i + 8j) m sâ€“1. Find
(a) the speed of the ball,
(b) the position vector of the ball after t seconds.
The point B on the field has position vector (10i + 7j) m.
(c) Find the time when the ball is due north of B.
At time t = 0, another player starts running due north from B and moves with constant
speed v m sâ€“1. Given that he intercepts the ball,
d) find the value of v.
I worked out part a, b, c but have no idea as to how to do part d :'(
Now just subtract your new position vector from the original position vector of B, and divide by the time it takes for that change to occur.
V=d/t
so v= change in position vector/t
Ask if you need more help. 
(Original post by nm786)
i'm guessing gradient represents acceleration?
Btw, could you please reply to my post: http://www.thestudentroom.co.uk/show...&postcount=309
thanks. 
(Original post by Pinkhead)
well, you've worked out the time when the ball is due north of B, so put that back into your position vector to find out where the ball actually is at that time.
Now just subtract your new position vector from the original position vector of B, and divide by the time it takes for that change to occur.
V=d/t
so v= change in position vector/t
Ask if you need more help. 
How would you determine if a 'particle' moves or not, when a force (ie a vertical force) is removed?
This has been asked in a few papers:
Jan 06 Q5
May 2002 Q4
I'm really confused, the markschemes not helpful. I know I need to find the new normal reaction...but from there I'm stuck :') 
(Original post by arnab)
sorry but y do you do the subtraction? can you explain that again? can you show it to me, step by step, as in the calculation?
Put that back into your position vector for the ball after t seconds:
That is the position vector of the ball at t=1.6. Call it rC
Now the distance between this position vector and the original point B is:
so
which gives us the distance of 6.8j
Now the other player moves with constant speed vms1. If the distance 6.8j is covered in 1.6 seconds, then

(Original post by Jukeboxing)
Yes, if the force PN or XN is applied horizontally then you should use cos(alpha) and sin(alpha).
So what you've done is correct on the diagram. 
(Original post by ninegrandstudent)
How would you determine if a 'particle' moves or not, when a force (ie a vertical force) is removed?
This has been asked in a few papers:
Jan 06 Q5
May 2002 Q4
I'm really confused, the markschemes not helpful. I know I need to find the new normal reaction...but from there I'm stuck :') 
(Original post by Pinkhead)
You basically work out the new friction force. If the friction force is greater than the force being applied in order to move the object, it will obviously not move. 
(Original post by ninegrandstudent)
Which force is applied to move the object though? Say if a vertical force was keeping it in place, and that is removed? Probably being really blonde and missing something obvious! 
(Original post by Pinkhead)
your answer for time should be 1.6 seconds.
Put that back into your position vector for the ball after t seconds:
That is the position vector of the ball at t=1.6. Call it rC
Now the distance between this position vector and the original point B is:
so
which gives us the distance of 6.8j
Now the other player moves with constant speed vms1. If the distance 6.8j is covered in 1.6 seconds, then

In this question, the unit vectors i and j are due east and due north respectively.]
A particle P is moving with constant velocity (â€“5i + 8j) m sâ€“1. Find
(a) the speed of P,
(b) the direction of motion of P, giving your answer as a bearing.
At time t = 0, P is at the point A with position vector (7i â€“ 10j) m relative to a fixed origin O. When t = 3 s, the velocity of P changes and it moves with velocity (ui + vj) m sâ€“1, where u and v are constants. After a further 4 s, it passes through O and continues to move with velocity (ui + vj) m sâ€“1.
(c) Find the values of u and v.
(d) Find the total time taken for P to move from A to a position which is due south of A.
Any idea on how to do part C and D 
(Original post by arnab)
In this question, the unit vectors i and j are due east and due north respectively.]
A particle P is moving with constant velocity (â€“5i + 8j) m sâ€“1. Find
(a) the speed of P,
(b) the direction of motion of P, giving your answer as a bearing.
At time t = 0, P is at the point A with position vector (7i â€“ 10j) m relative to a fixed origin O. When t = 3 s, the velocity of P changes and it moves with velocity (ui + vj) m sâ€“1, where u and v are constants. After a further 4 s, it passes through O and continues to move with velocity (ui + vj) m sâ€“1.
(c) Find the values of u and v.
(d) Find the total time taken for P to move from A to a position which is due south of A.
Any idea on how to do part C and D 
(Original post by arnab)
In this question, the unit vectors i and j are due east and due north respectively.]
A particle P is moving with constant velocity (â€“5i + 8j) m sâ€“1. Find
(a) the speed of P,
(b) the direction of motion of P, giving your answer as a bearing.
At time t = 0, P is at the point A with position vector (7i â€“ 10j) m relative to a fixed origin O. When t = 3 s, the velocity of P changes and it moves with velocity (ui + vj) m sâ€“1, where u and v are constants. After a further 4 s, it passes through O and continues to move with velocity (ui + vj) m sâ€“1.
(c) Find the values of u and v.
(d) Find the total time taken for P to move from A to a position which is due south of A.
Any idea on how to do part C and D
It then moves with velocity ui + vj for 4 seconds passing through the origin, so
So
So and 
(Original post by Pinkhead)
In question 5 from the jan 06 paper, the force pulling the object down the plane once the horizontal force is removed is the component of the weight, i.e. 10sin30. 
Soooo....who else is utterly screwed for this?

(Original post by arnab)
In this question, the unit vectors i and j are due east and due north respectively.]
A particle P is moving with constant velocity (â€“5i + 8j) m sâ€“1. Find
(a) the speed of P,
(b) the direction of motion of P, giving your answer as a bearing.
At time t = 0, P is at the point A with position vector (7i â€“ 10j) m relative to a fixed origin O. When t = 3 s, the velocity of P changes and it moves with velocity (ui + vj) m sâ€“1, where u and v are constants. After a further 4 s, it passes through O and continues to move with velocity (ui + vj) m sâ€“1.
(c) Find the values of u and v.
(d) Find the total time taken for P to move from A to a position which is due south of A.
Any idea on how to do part C and D
so if the origin is 0,0 the position vector must be 0.
position vector= original position + velocity x time
so
equate i and j to 0 to find u and v
d) position vector after t seconds is
group the components:
if P is due south of A, you can equate the i components of the position vector with the i component of A, which is 7i:
Now add this onto the time before the velocity changes (3 seconds) and you'll get 10.5seconds. 
(Original post by oli_G)
So you know the position vector of P is (7i  10j)m and it moves with a velocity of (5i + 8j)m/s for the first 2 seconds. So the displacement of P when t=3 is
(710) i + (10 + 16)j = (3i + 6j) m
It then moves with velocity ui + vj for 4 seconds passing through the origin, so
So
So and