# A level north west regional mock gce 2022 mathematics with mechanics 3

### A level north west regional mock gce 2022 mathematics with mechanics 3

A level north west regional mock gce 2022 mathematics with mechanics 3

The particles A and B have position vectors nt time ( seconds given by rA = ti +(t 2 – 2i)j and
rn = (/-2)i + (r -6/)jrespectively.
i) How for apart arc the particles initially?
in ‘ Vri ) Deduce ‘T’ that , *Cifvolocily the particles B relative have thetosame A ismass a constant , then they produce the sam e force,
iv) ow that the path of the particles is parabolic
1

“• ^’s P-i-ted vertically upwards from a point O with speed30/a /.1.
**me ^ t!t^es to attain maximum height above O
(u) the maximum height above O it attains
.!’e i-y scc°nds after A was projected from 0, another particle B was dropped from 0;
(m) calculate the height, h above O at which A was, and its speed, just before B was dropped

(iv) show that the particles collide -s after B was dropped. (4mks)
4
25
Hence or otherwise, show that the particles collide at a depth d -— m below O. (2mks)
(g = 10m/s2)
3. (a) The figure below represents a uniform rectangular plate ABCD of length 12a and width10a.
A portion of the plate in the shape of an isosceles triangle DEC, with DE= EC =13a is cut out and