1.10 Vectors

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Question 98

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.

[2]

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.

[1]

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.

[4]

1.10 Vectors

Question 98

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.

[2]

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.

[1]

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.

[4]

1.10 Vectors

Question 98

Markscheme

1.10 Vectors

Question 98

Markscheme

1.10 Vectors

Question 98

1.10 Vectors Questions

1.10 Vectors

Question 98

1.10 Vectors Questions