Skip to content

Course home

Sign up

4 Unit A2 2: Applied Mathematics (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258
Question 54

At 10 a.m. a plane A A\,A has position vector (2i−5j)(2\mathbf{i} - 5\mathbf{j})(2i−5j) km and moves with constant velocity (−4i+6j)(-4\mathbf{i} + 6\mathbf{j})(−4i+6j) km h−1^{-1}−1.

At the same time a plane B B\,B has position vector (−3i−9j)(-3\mathbf{i} - 9\mathbf{j})(−3i−9j) km and moves with constant velocity (i+8j)(\mathbf{i} + 8\mathbf{j})(i+8j) km h−1^{-1}−1.

The unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.

a.

Find the position vector of A A\,A relative to B B\,B at t t\,t hours after 10 a.m.

[3]
b.

Find the time at which A A\,A is due west of BBB.

[2]
c.

Find the time, after 10 a.m., at which the planes are exactly 37 km apart.

[4]
Markscheme

4 Unit A2 2: Applied Mathematics (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4 Unit A2 2: Applied Mathematics (A-level only)

Question bank