Parametric equations in modellingEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

What does the parameter usually represent in a modelling question?
Equations for constant velocity (u,v) from (x0,y0)?
How do you find the velocity from two positions at two times?
Moves from (1,8) at t=0 to (6,20) at t=5. Position at time t?
How do you find speed from a velocity (u,v)?
How do you find when a projectile lands?
How do you find the greatest height of y=at-bt^2?
What is the range of a projectile?
Period of x=r\sin(\omega t), y=-r\cos(\omega t)?
What conditions are needed for two objects to collide?
Can two paths cross without a collision?
How do you find the minimum distance between two moving objects?

Exam questions on Parametric equations in modelling

A drone moves in a straight line at constant velocity. Relative to a fixed origin it is at the point $(2,10)$ when $t=0$ and at the point $(14,34)$ when $t=4$ , where $t$ is the time in seconds and distances are in metres.
The drone reaches the line $x=20$ . Find the time at which this happens and the $y$ -coordinate of the drone at that time.2 marks
A seat on a Ferris wheel moves so that at time $t$ minutes, $t\ge0$ , its position is modelled by $x=15\sin\left(\frac{\pi t}{2}\right)$ , $y=16-15\cos\left(\frac{\pi t}{2}\right)$ , where $x$ is the horizontal distance in metres from the vertical line through the centre of the wheel and $y$ is the height in metres above the ground.
Find a Cartesian equation for the path of the seat.2 marks
A ball is kicked from the ground at time $t=0$ seconds. Until it returns to the ground, its position in metres is modelled by $x=12t$ , $y=9t-5t^2$ , where $x$ is the horizontal distance from the kick and $y$ is the height above the ground.
Find the time for which the ball is in the air, and the horizontal distance it travels in this time.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).