Parametric equations in modellingEdexcel A-Level Maths: Mind map

Exam questions on Parametric equations in modelling

1. 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
2. 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
3. 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