Motion in a vertical plane and projectilesEdexcel International A Level Further Maths: Mind map

Exam questions on Motion in a vertical plane and projectiles

1. A ball is thrown vertically upwards with speed $14\text{ m s}^{-1}$ from a point $2$ m above horizontal ground. The ball is modelled as a particle moving freely under gravity. Take $g=9.8\text{ m s}^{-2}$.
   Find the speed of the ball as it hits the ground.2 marks
2. A particle is projected from a point $O$ on horizontal ground with speed $28\text{ m s}^{-1}$ at an angle $\alpha$ above the horizontal, where $\sin\alpha=\frac35$. The particle moves freely under gravity and does not hit anything before it lands. Take $g=9.8\text{ m s}^{-2}$.
   Find the horizontal distance from $O$ to the point where the particle lands.2 marks
3. A stone is thrown from the top of a vertical cliff, $40$ m above horizontal sea level, with speed $20\text{ m s}^{-1}$ at $30^\circ$ above the horizontal. The stone is modelled as a particle moving freely under gravity. Take $g=9.8\text{ m s}^{-2}$.
   Find the time taken for the stone to reach the sea.3 marks