Motion in a vertical plane and projectilesEdexcel International A Level Further Maths: Subtopic test

1. 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 $g=9.8\text{ m s}^{-2}$.

   (a)

   What is the greatest height of the ball above the ground?

   [1 mark]

   • A$10$ m
   • B$5$ m
   • C$20$ m
   • D$12$ m

   (b)

   How long after being thrown does the ball hit the ground, to 2 significant figures?

   [1 mark]

   • A$1.4$ s
   • B$3.0$ s
   • C$2.9$ s
   • D$2.7$ s

   (c)

   Find the speed of the ball as it hits the ground.

   [2 marks]

   Total for question 1: 4 marks

2. 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 $g=9.8\text{ m s}^{-2}$.

   (a)

   What is the greatest height reached above $O$?

   [1 mark]

   • A$14.4$ m
   • B$40$ m
   • C$7.2$ m
   • D$25.6$ m

   (b)

   How long is the particle in the air, to 2 significant figures?

   [1 mark]

   • A$1.7$ s
   • B$2.9$ s
   • C$3.4$ s
   • D$5.7$ s

   (c)

   Find the horizontal distance from $O$ to the point where the particle lands.

   [2 marks]

   Total for question 2: 4 marks

3. 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 $g=9.8\text{ m s}^{-2}$.

   (a)

   Find the time taken for the stone to reach the sea.

   [3 marks]

   (b)

   Find the horizontal distance from the foot of the cliff to the point where the stone lands, and the speed of the stone as it lands.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A ball is kicked from a point $O$ on horizontal ground with speed $25\text{ m s}^{-1}$ at an angle $\theta$ above the horizontal, where $\tan\theta=\frac43$. A vertical fence $12$ m high stands on the ground $30$ m horizontally from $O$, in the plane of the ball's motion. The ball is modelled as a particle moving freely under gravity. Take $g=9.8\text{ m s}^{-2}$.

   (a)

   Show that the ball passes over the fence, and find the vertical distance between the ball and the top of the fence as it passes over it.

   [6 marks]

   (b)

   The ball lands on the ground beyond the fence. Find the distance from $O$ to the landing point, and the angle the path makes with the ground as the ball lands.

   [6 marks]

   Total for question 4: 12 marks

End of questions