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The question involves a man falling with a parachute from a height of 50 meters, initially in free fall for 2 seconds before reaching terminal velocity of 2 m/s. A stone is dropped 13 seconds after the man starts falling. We are tasked with finding which object (parachute or stone) will hit the ground first.

### Step-by-step analysis:

1. **Man with parachute:**
   - **First 2 seconds of free fall:**
     - During free fall, the man is only under gravity. The formula for the distance fallen during this period is:
       \[
       s = \frac{1}{2} g t^2
       \]
       where \( g = 9.8 \, \text{m/s}^2 \) and \( t = 2 \, \text{seconds} \).
       Substituting:
       \[
       s = \frac{1}{2} \times 9.8 \times 2^2 = 19.6 \, \text{meters}.
       \]
       So, after 2 seconds, the man has fallen 19.6 meters.
       
   - **Remaining height:**
     \[
     \text{Remaining height} = 50 - 19.6 = 30.4 \, \text{meters}.
     \]
     After 2 seconds, the man reaches terminal velocity (2 m/s) and continues to fall at this constant speed.

   - **Time to fall remaining distance:**
     The time to cover the remaining 30.4 meters at terminal velocity can be calculated as:
     \[
     t_{\text{terminal}} = \frac{\text{distance}}{\text{velocity}} = \frac{30.4}{2} = 15.2 \, \text{seconds}.
     \]

   - **Total time for man with parachute:**
     \[
     t_{\text{man}} = 2 \, \text{seconds (free fall)} + 15.2 \, \text{seconds (at terminal velocity)} = 17.2 \, \text{seconds}.
     \]

2. **Stone:**
   The stone is dropped 13 seconds after the man. It is in free fall the entire time, so the time for the stone to reach the ground can be calculated using the equation:
   \[
   s = \frac{1}{2} g t^2,
   \]
   where \( s = 50 \, \text{meters} \) and \( g = 9.8 \, \text{m/s}^2 \). Solving for \( t \):
   \[
   50 = \frac{1}{2} \times 9.8 \times t^2 \implies t^2 = \frac{100}{9.8} \implies t = \sqrt{10.2} \approx 3.2 \, \text{seconds}.
   \]

   Since the stone is dropped 13 seconds after the man, the total time for the stone is:
   \[
   t_{\text{stone}} = 13 + 3.2 = 16.2 \, \text{seconds}.
   \]

### Conclusion:
- The man with the parachute takes 17.2 seconds to reach the ground.
- The stone takes 16.2 seconds to reach the ground.

Thus, **the stone will reach the ground first**, and the correct answer is **A. Stone will reach the ground first**.

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Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. How does terminal velocity affect objects of different masses?
2. What would happen if the man did not have a parachute? How would his fall time change?
3. Can you calculate the velocity of the stone just before it hits the ground?
4. What factors influence the terminal velocity of a falling object?
5. How would air resistance impact the time taken for both objects to reach the ground?

**Tip:** When calculating free fall times, always make sure to account for any changes in velocity, such as reaching terminal velocity, which can dramatically alter the outcome.

A man of mass 100 kg along with a light parachute dropped from a tower of height 50 m. It falls freely under gravity for 2 seconds, then almost immediately attains terminal velocity 2 m/s. A stone is dropped from the tower 13 seconds later (from the man). Which object will reach the ground first?

Solve a physics problem involving a man with a parachute falling from a height of 50 meters and reaching terminal velocity after 2 seconds. Learn the kinematic equations used to determine which object, the man or the stone, hits the ground first.

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