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rt 4: Free Fall, Air Resistance & Relative Motion

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  1. A ball is dropped from rest from the top of a 45 m tower. Ignoring air resistance, calculate (a)

the time to reach the ground and (b) its speed at impact.

  1. A hammer and a feather are released together from the same height on the Moon, where there

is no atmosphere. Which lands first? Explain using the idea of acceleration due to gravity.

Verified Answer :

Final answer:

The ball takes approximately 3.02 seconds to reach the ground with a speed of around 29.6 m/s at impact. Both the hammer and feather released on the Moon fall simultaneously, without being affected by air resistance. This illustrates concepts of free fall and acceleration due to gravity in an ideal environment.


Explanation:

Free Fall and Motion in Physics

This question involves understanding the concepts of free fall, acceleration due to gravity, and how air resistance affects the motion of objects.

1. Ball Dropped from a Tower

  1. (a) Time to Reach the Ground: When a ball is dropped from rest, it accelerates downward due to the force of gravity. The formula for the time (t) of free fall is given by the equation:
    h = (1/2)gt²,
    where h is the height (45 m), g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time in seconds. Rearranging this gives us:
    t² = (2h)/g
    Substituting the values, we find:
    t² = (245 m)/(9.81 m/s²)
    t² = 9.16
    t ≈ 3.02 seconds.
  2. (b) Speed at Impact: The final speed (v) of the ball just before impact can be calculated using the formula:
    v = gt
    where t is the time calculated previously. Thus:
    v = 9.81 m/s² 3.02 s ≈ 29.6 m/s    .

2. Hammer and Feather on the Moon

On the Moon, where there is no atmosphere, both the hammer and the feather are expected to fall at the same rate due to gravity. The absence of air resistance allows them to experience the same acceleration of approximately 1.625 m/s². Therefore, they will land at the same time despite their different weights because their motion is only influenced by gravity.


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