Two drones, Phoenix and Icarus, are performing a synchronized survey of a forest fire. Both drones fly in the same direction along straight, parallel paths at a constant altitude.

Phoenix maintains a constant velocity of $s−1(3\mathbf{i} + 4\mathbf{j})\text{ m s}^{-1}$ .

At time $t = 0$ seconds, Icarus is at the position $metres(7\mathbf{i} - 24\mathbf{j})\text{ metres}$ and is moving with a constant speed of $s−115\text{ m s}^{-1}$ .

(i) Explain why Icarus's velocity must be of the form $s−1k(3\mathbf{i} + 4\mathbf{j})\text{ m s}^{-1}$ , where $k$ is a constant.

(ii) Show that $k = 3$ .

Determine the position vector of Icarus when $t = 2$ .

At both $t = 0$ and $t = 2$ , the distance between Phoenix and Icarus is $metres26\text{ metres}$ .

Calculate the shortest distance between their two parallel lines of flight.

Fully justify your answer.

Two drones, Phoenix and Icarus, are performing a synchronized survey of a forest fire. Both drones fly in the same direction along straight, parallel paths at a constant altitude.

Phoenix maintains a constant velocity of $s−1(3\mathbf{i} + 4\mathbf{j})\text{ m s}^{-1}$ .

At time $t = 0$ seconds, Icarus is at the position $metres(7\mathbf{i} - 24\mathbf{j})\text{ metres}$ and is moving with a constant speed of $s−115\text{ m s}^{-1}$ .

(i) Explain why Icarus's velocity must be of the form $s−1k(3\mathbf{i} + 4\mathbf{j})\text{ m s}^{-1}$ , where $k$ is a constant.

(ii) Show that $k = 3$ .

Determine the position vector of Icarus when $t = 2$ .

At both $t = 0$ and $t = 2$ , the distance between Phoenix and Icarus is $metres26\text{ metres}$ .

Calculate the shortest distance between their two parallel lines of flight.

Fully justify your answer.

1.10 Vectors

Question 10

Markscheme

1.10 Vectors

Question 10

Markscheme

1.10 Vectors

Question 10

1.10 Vectors Questions

1.10 Vectors

Question 10

1.10 Vectors Questions