An 80 kg person is parachuting and is experiencing a downward acceleration of `"2.8 m s"^(-2)`. The mass of the parachute is 5 kg. If the upward force on the open parachute is `kxx10^(2)N`, then what is the value of k? `("Take "g=9.8ms^(-2))`

Answer

To solve the problem, we need to analyze the forces acting on the person with the parachute and apply Newton's second law of motion.

### Step-by-Step Solution:

1. **Identify the total mass**:
The total mass \( m \) of the person and the parachute is:
\[ m = 80 \, \text{kg} + 5 \, \text{kg} = 85 \, \text{kg} \]

2. **Calculate the weight**:
The weight \( W \) acting downward is given by:
\[ W = mg = 85 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 833 \, \text{N} \]

3. **Set up the equation of motion**:
According to Newton's second law, the net force acting on the system is equal to the mass times the acceleration. The equation can be written as:
\[ W - F = ma \]
where \( F \) is the upward force due to the parachute, and \( a \) is the downward acceleration.

4. **Substitute the known values**:
We know \( W = 833 \, \text{N} \), \( F = k \times 10^2 \, \text{N} \), \( m = 85 \, \text{kg} \), and \( a = 2.8 \, \text{m/s}^2 \). Substituting these into the equation gives:
\[ 833 \, \text{N} - k \times 10^2 = 85 \, \text{kg} \times 2.8 \, \text{m/s}^2 \]

5. **Calculate the right-hand side**:
\[ 85 \, \text{kg} \times 2.8 \, \text{m/s}^2 = 238 \, \text{N} \]

6. **Rearrange the equation**:
Now we can rearrange the equation:
\[ 833 \, \text{N} - 238 \, \text{N} = k \times 10^2 \]
\[ 595 \, \text{N} = k \times 10^2 \]

7. **Solve for \( k \)**:
Dividing both sides by \( 10^2 \) gives:
\[ k = \frac{595 \, \text{N}}{100} = 5.95 \]

### Final Answer:
The value of \( k \) is \( 5.95 \).

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