Weight and motion under gravityEdexcel A-Level Maths: Subtopic test

1. 1
   A ball is thrown vertically upwards with speed $14$ m s$^{-1}$ from ground level. Model the ball as a particle moving freely under gravity, with $g=9.8$ m s$^{-2}$.

   (a)

   Find the greatest height of the ball above the ground.

   [1 mark]

   • A$20$ m
   • B$1.43$ m
   • C$28.6$ m
   • D$10$ m

   (b)

   Find the total time for which the ball is in the air before it returns to the ground.

   [1 mark]

   • A$1.43$ s
   • B$5.71$ s
   • C$2.86$ s
   • D$10$ s

   (c)

   Find the speed of the ball when it is $4$ m above the ground on its way down.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A coin is dropped from rest from a bridge, $40$ m above the surface of a river. Model the coin as a particle moving freely under gravity, with $g=9.8$ m s$^{-2}$.

   (a)

   Find the time taken for the coin to reach the river.

   [1 mark]

   • A$4.08$ s
   • B$2.86$ s
   • C$8.16$ s
   • D$1.43$ s

   (b)

   Find the speed of the coin as it reaches the river.

   [1 mark]

   • A$28$ m s$^{-1}$
   • B$784$ m s$^{-1}$
   • C$19.8$ m s$^{-1}$
   • D$40.0$ m s$^{-1}$

   (c)

   Find the distance the coin falls in the last second before it reaches the river.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A ball is thrown vertically upwards with speed $15$ m s$^{-1}$ from a point $1.5$ m above horizontal ground. Model the ball as a particle moving freely under gravity, with $g=9.8$ m s$^{-2}$.

   (a)

   Find the greatest height of the ball above the ground.

   [3 marks]

   (b)

   Find the time from projection until the ball hits the ground.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A stone of mass $0.2$ kg is thrown vertically upwards with speed $8$ m s$^{-1}$ from ground level. There is no air resistance and the stone is modelled as a particle. The acceleration due to gravity is $1.6$ m s$^{-2}$ on the Moon and $9.8$ m s$^{-2}$ on Earth.

   (a)

   The stone is thrown on the Moon.
   (i) Find the greatest height reached by the stone.
   (ii) Find the time taken for the stone to return to the surface.
   (iii) Find the weight of the stone on the Moon and its weight on Earth.

   [6 marks]

   (b)

   (i) The stone is thrown with the same speed from the surface of the Earth. Find the greatest height reached and the time taken to return to the ground.
   (ii) A student says: 'The stone goes higher on the Moon because it has less mass there.' Evaluate this statement.

   [6 marks]

   Total for question 4: 12 marks

End of questions