Pregunta
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(30) A man drops a bag out a window 11 meters above ground to his friend, 1.7 meters above ground. Determine the velocity of the bag just before it reaches his friend’s hands.
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Ask by Mcdonald Cole. in the United States
Jan 23,2025

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The bag reaches the friend’s hands with a velocity of approximately 13.5 meters per second.

Solución

To determine the velocity of the bag just before it reaches the friend’s hands, we can analyze the problem using the principles of kinematics under free fall. Here’s a step-by-step solution:

Given:

  • Mass of the bag (m): (Note: The mass is not required for calculating velocity in free fall without air resistance.)
  • Initial height above ground (h₁):
  • Final height above ground (h₂):
  • Acceleration due to gravity (g): ²

Steps:

  1. Calculate the Drop Distance (Δh):
  2. Determine Initial Velocity (u):
    Since the bag is dropped, its initial velocity .
  3. Use the Kinematic Equation:
    The final velocity can be found using the equation:
    ²²
    Plugging in the known values:
    ²²
    ²²²
  4. Solve for :
    (For a more precise calculation: )

Conclusion:

The velocity of the bag just before it reaches the friend’s hands is approximately 13.5 meters per second.
Final Answer:
The bag strikes the friend’s hands with a velocity of approximately 13.5 m s⁻¹.

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Extra Insights

To find the velocity of the bag just before it reaches his friend’s hands, we can use the principle of conservation of mechanical energy. The potential energy lost by the bag will convert into kinetic energy. The initial height of the bag is and the height of the friend is . The height it falls is:
The potential energy at the initial height is given by:
where (acceleration due to gravity) is approximately . The change in potential energy when moving from height to height is converted into kinetic energy (KE):
Setting the change in potential energy equal to kinetic energy, we have:
Cancelling from both sides (since is not zero) gives:
Solving for , we get:
Substituting in the values:
Thus, the velocity of the bag just before it reaches his friend’s hands is approximately .

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