m1 mechanics as vectors 2018 internation edexcel q6

part a is easy. A particle of mass 2 kg moves under the action of two forces 2 (2i and 3j) N and (4i-5j)N. find a, which is 3.2 (root10)

part b doesn't make sense. at t = 0, P has velocity (-ui + uj) ms-1 where u is a positive constant. at t = T, P has velocity (10i + 2j) ms-1

find:
value of T
value of u
*********end*********

why did they split the vectors?

**ms working**
10i + 2j = (-ui + uj) + (3i - j)T
10 = -u + 3T
2 = u -T

T = 6
u = 8

(edited 1 month ago)

Reply 1

mqb2766

Original post by simple123site

part a is easy. A particle of mass 2 kg moves under the action of two forces 2 (2i and 3j) N and (4i-5j)N. find a, which is 3.2 (root10)
part b doesn't make sense. at t = 0, P has velocity (-ui + uj) ms-1 where u is a positive constant. at t = T, P has velocity (10i + 2j) ms-1
find:
value of T
value of u
*********end*********
why did they split the vectors?
**ms working**
10i + 2j = (-ui + uj) + (3i - j)T
10 = -u + 3T
2 = u -T
T = 6
u = 8

The components of the vector (the i "horizontal" and the j "vertical") are independent and both must be satisfied for the vector equation to be satisfied. So the original vector equation really contains two simultaneous equations in the two variables u and T which is what you need.

(edited 1 month ago)

Reply 2

simple123site

Original post by mqb2766

i can assume this can also be done for a question involving acceleration , Forces and displacement ? (forming simultaneous equations) and using suvat equations?

Reply 3

mqb2766

Original post by simple123site

i can assume this can also be done for a question involving acceleration , Forces and displacement ? (forming simultaneous equations) and using suvat equations?

Of course, the i and j directions (Cartesian coordinates) are independent/orthogonal so they can be analysed seperately, whatever the equation represents.

As a way to picture it, the balls motion in the horizontal and vertical directions are independent when its fired

You have constant horizontal speed which is maintained when the ball is fired upwards (gravity causes parabolic motion) and each direction can be analysed seperately using suvat. Using vectors/Cartesian coordinates

you can write it all down as a single equation but in reality it contains seperate coordinates (2, 3 or ...) which are represented by the i,j,k vectors/directions.