Two drones, Alpha and Beta, travel along straight-line paths in a horizontal surveying area.

Drone Alpha maintains a constant velocity of $s−1(9\mathbf{i} + 12\mathbf{j}) \text{ m s}^{-1}$ .

Drone Beta travels from the position vector $(−5i+10j)(-5\mathbf{i} + 10\mathbf{j})$ metres to the position vector $(22i+46j)(22\mathbf{i} + 46\mathbf{j})$ metres over a duration of 6 seconds.

Show that the direction of motion of Beta is parallel to the direction of motion of Alpha.

A technician suggests that Beta must be moving with a constant velocity of $s−1(4.5\mathbf{i} + 6\mathbf{j}) \text{ m s}^{-1}$ . Explain why this statement might be false.

A third drone, Gamma, flies at a constant speed of $\text{ m s}^{-1}$ along a separate straight path. The flight paths of Alpha and Gamma intersect at a fixed waypoint $X$ .

It is recorded that:

Alpha reaches $X$ exactly 4 seconds after Gamma has passed through $X$ .
At a timestamp 8 seconds after Gamma has passed through $X$ , the distance between the two drones is exactly 100 metres.

Demonstrate that the flight paths of Alpha and Gamma are perpendicular.

Two drones, Alpha and Beta, travel along straight-line paths in a horizontal surveying area.

Drone Alpha maintains a constant velocity of $s−1(9\mathbf{i} + 12\mathbf{j}) \text{ m s}^{-1}$ .

Drone Beta travels from the position vector $(−5i+10j)(-5\mathbf{i} + 10\mathbf{j})$ metres to the position vector $(22i+46j)(22\mathbf{i} + 46\mathbf{j})$ metres over a duration of 6 seconds.

Show that the direction of motion of Beta is parallel to the direction of motion of Alpha.

A technician suggests that Beta must be moving with a constant velocity of $s−1(4.5\mathbf{i} + 6\mathbf{j}) \text{ m s}^{-1}$ . Explain why this statement might be false.

A third drone, Gamma, flies at a constant speed of $\text{ m s}^{-1}$ along a separate straight path. The flight paths of Alpha and Gamma intersect at a fixed waypoint $X$ .

It is recorded that:

Alpha reaches $X$ exactly 4 seconds after Gamma has passed through $X$ .
At a timestamp 8 seconds after Gamma has passed through $X$ , the distance between the two drones is exactly 100 metres.

Demonstrate that the flight paths of Alpha and Gamma are perpendicular.

2.2 Kinematics

Question 58

Markscheme

2.2 Kinematics

Question 58

Markscheme

2.2 Kinematics

Question 58

2.2 Kinematics Questions

2.2 Kinematics

Question 58

2.2 Kinematics Questions