Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.12—vector Applications to Kinematics with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.12—vector Applications to Kinematics and mirrors Paper 1, 2, 3 style where relevant.
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A survey drone is monitored from a fixed launch point. Its position relative to the launch point at time seconds is given by . The components represent easting (m), northing (m), and height above the launch point (m).
Determine the speed of the drone.
Calculate the distance of the drone from the launch point when .
Calculate the compass bearing on which the drone is travelling.
A survey drone releases a sensor pod. Its position vector relative to a fixed origin , at time seconds (), is described by , where the -axis is vertical and all distances are in metres.
Demonstrate that the sensor pod moves in a vertical plane and specify an equation of this plane.
Determine a vector expression for the velocity of the sensor pod at time .
By calculating the scalar product, verify that the velocity of the sensor pod is orthogonal to the normal vector of this plane at all times.
Find a vector expression for the acceleration of the sensor pod at time .
Calculate the time when the sensor pod passes the point .
Determine the speed of the sensor pod as it passes this point.
A particle moves in a plane such that its position vector (in metres) at time seconds, for , is given by .
Find the velocity vector, , of the particle in terms of .
Find the position vector of the particle at the instant its speed is at a minimum.
On a transport graph, a drone has position vector (in metres) relative to vertex at time seconds, for , given by .
Find the velocity vector, , in terms of .
Find the position vector of the drone at the instant its speed is at a minimum.
An inspection drone in a warehouse has position coordinates , where and are the horizontal displacements from the centre of a charging pad on the warehouse floor and is the height above the floor. All distances are in metres.
At 14:30, the drone is at . At 14:32, it is at . Let be the time in minutes after 14:30.
Assume the drone continues to move in a straight line with constant velocity.
When it reaches a height of m, it keeps the same horizontal motion but changes its rate of descent so that it arrives exactly at .
Formulate a vector equation for the position of the drone as a function of .
Demonstrate that the drone's path goes directly over the charging pad.
Determine the drone's height as it passes over the charging pad.
Calculate the specific time it passes over the charging pad.
Identify the time when the drone is m above the warehouse floor.
Calculate the Euclidean distance between the drone and the charging pad at that moment.
If the drone's velocity becomes after adjusting its descent, determine the constant .