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IB Maths AI HL Ahl 3 12 Hl Vector Kinematics Questions

Practise modelling constant-velocity motion with vector equations, solving intersections or closest approach, and checking time, units, direction and physical meaning.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Model constant-velocity motion in 2D or 3D with r=r₀+vt and calculate a position at a stated time.
  • Solve for intersections, closest-approach time or distance and other kinematic parameters from vector equations.
  • Use variable-velocity, projectile or circular special cases to interpret a path, rate or limiting condition.
  • Check time, units, direction and the physical meaning of the resulting position or distance.

Learn this topic

Study AHL 3.12 (HL)—Vector kinematics conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Ahl 3 12 Hl Vector Kinematics Questions question 1

[Maximum number: 8]

In this question, all distances are in kilometres and t is in hours.
Let (100)\left(\begin{smallmatrix}1\\0\\0\end{smallmatrix}\right) be a displacement of 1 km due east, (010)\left(\begin{smallmatrix}0\\1\\0\end{smallmatrix}\right) be a displacement of 1 km due north, and (001)\left(\begin{smallmatrix}0\\0\\1\end{smallmatrix}\right) be a vertical displacement of 1 km.
Highway 85 in Saudi Arabia is a long, straight, flat road.
Relative to the centre of the town Arar, point O, the position vector of a car, C, travelling along this road is given by:

OC→=(10−50)+t(50−330)\overrightarrow{\mathrm{OC}}=\left(\begin{array}{c}10\\-5\\0\end{array}\right)+t\left(\begin{array}{c}50\\-33\\0\end{array}\right)

The police are testing a long-range drone, D, to monitor cars travelling along this road. The drone is launched at t=0 from the point with position vector (200−1000.02)\left(\begin{smallmatrix}200\\-100\\0.02\end{smallmatrix}\right) and flies in a straight line with a constant height of 0.02 km and a constant velocity of (−15−200)\left(\begin{smallmatrix}-15\\-20\\0\end{smallmatrix}\right).

Question (a)

(a)

Write down the position vector, OD→\overrightarrow{\mathrm{OD}}, of the drone at time t.

[ 1 ]

Question (b)

(b)

At time t1t_1, the drone passes through the point with position vector (152p0.02)\left(\begin{smallmatrix}152\\p\\0.02\end{smallmatrix}\right).
Find the value of

[ 3 ]

Question (i)

(i)

t1t_{1}

[ 2 ]

Question (ii)

(ii)

p.

[ 1 ]

Question (c)

(c)

Hence, find the shortest distance between the car and the drone.

[ 4 ]
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