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Space, time and motion · Question 8

Space, time and motion · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
11
Topics
2
Answer
Complete
Ball thrown horizontally from the top of a buildingbuilding25 m12 m s⁻¹ball, mass 0.150 kg
Figure 3Side view. A building stands on level hatched ground, its height marked by a dimension line labelled 25 m running from roof level down to the ground. A small ball, labelled as having mass 0.150 kg, sits at the right-hand edge of the roof, and a horizontal arrow from the ball labelled 12 m s⁻¹ points away from the building. A faint dashed curve traces the path the ball follows from the roof edge down to the ground.
structured11 marks

A ball of mass 0.150 kg is thrown horizontally at 12 m s⁻¹ from the top of a building 25 m high. Air resistance is negligible until part (d).

  1. (a)

    Calculate Calculate the time taken for the ball to reach the ground.

    2 marks
  2. (b)

    Determine Determine the speed of the ball as it reaches the ground.

    3 marks
  3. (c)

    Determine Determine the magnitude of the impulse delivered to the ball by gravity during its flight.

    2 marks
  4. (d)

    Explain In reality air resistance is not negligible. Explain how the horizontal distance travelled and the time of flight each differ from the values calculated above.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: 25 = ½ × 9.81 × t² t = 2.26 s vertical component v_y = 9.81 × 2.26 = 22.2 m s⁻¹
01

(a)

2 marks

Calculate Calculate the time taken for the ball to reach the ground.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    25 = ½ × 9.81 × t²

  2. 2

    t = 2.26 s

02

(b)

3 marks

Determine Determine the speed of the ball as it reaches the ground.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    vertical component v_y = 9.81 × 2.26 = 22.2 m s⁻¹

  2. 2

    horizontal component is unchanged at 12 m s⁻¹

  3. 3

    speed = √(12² + 22.2²) = 25 m s⁻¹

03

(c)

2 marks

Determine Determine the magnitude of the impulse delivered to the ball by gravity during its flight.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    impulse = change in momentum = m × change in vertical velocity = 0.150 × 22.2

  2. 2

    impulse = 3.3 N s, directed vertically downwards

04

(d)

4 marks

Explain In reality air resistance is not negligible. Explain how the horizontal distance travelled and the time of flight each differ from the values calculated above.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    air resistance acts opposite to the velocity, so it has both a horizontal and a vertical component throughout the flight

  2. 2

    the horizontal component decelerates the ball, so the horizontal velocity is no longer constant and the horizontal distance is smaller

  3. 3

    the vertical component acts upward as the ball falls, reducing the downward acceleration below g

  4. 4

    so the ball takes longer to fall the same 25 m, and the time of flight increases

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