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Difficulty: EasyGravity and Free Fall

A stationary drone drops a 5 kg5\text{ kg} supply package from a high altitude. Ignoring air resistance and assuming the acceleration due to gravity is 10 m/s210\text{ m/s}^2, what is the downward velocity of the package after it has been falling for exactly 4 seconds4\text{ seconds}?

  1. A
    80 m/s80\text{ m/s}
  2. B
    50 m/s50\text{ m/s}
  3. 40 m/s40\text{ m/s}Answer
  4. D
    8 m/s8\text{ m/s}

Answer

The downward velocity of the package is 40 m/s40\text{ m/s}.
In free fall without air resistance, velocity increases at a constant rate equal to gravitational acceleration, regardless of mass. Multiplying the acceleration (10 m/s210\text{ m/s}^2) by the time (4 seconds4\text{ seconds}) gives the correct velocity of 40 m/s40\text{ m/s}.

Step-by-Step Solution

1
Identify the given values from the problem statement.
Initial velocity (v0v_0) = 0 m/s0\text{ m/s}, Acceleration (gg) = 10 m/s210\text{ m/s}^2, Time (tt) = 4 s4\text{ s}, Mass (mm) = 5 kg5\text{ kg}.
Extracting variables is the necessary first step to choosing the correct kinematic formula.
2
Select the correct formula to find the final velocity.
Use the formula v=v0+gtv = v_0 + gt.
This formula relates velocity, acceleration, and time without needing the fall distance.
3
Substitute the values into the formula and solve.
v=0+(10×4)=40 m/sv = 0 + (10 \times 4) = 40\text{ m/s}.
Performing the calculation yields the final velocity. The mass of 5 kg5\text{ kg} is irrelevant because all objects in free fall accelerate at the same rate in the absence of air resistance.

Key Concept

In free fall with no air resistance, the velocity of an object increases linearly with time (v=gtv = gt), completely independent of the object's mass.
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Topics

Gravity and Free Fall

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