A paraglider is flying horizontally at a constant speed. Assume that only two forces act on it in the vertical direction, its weight and a vertical lift force exerted on its wings by the air. The lift force has a magnitude of 1800 N. If the lift force should suddenly decrease to 1200 N, what would be the vertical acceleration of the glider? For question, take the upward direction to be the +y direction.

Options

A. `-0.67" m"//"s"^(2)`
B. `-3.3" m"//"s"^(2)`
C. `-4.9" m"//"s"^(2)`
D. `-6.6" m"//"s"^(2)`

Answer

To find the vertical acceleration of the paraglider when the lift force decreases, we can follow these steps:

### Step 1: Identify the forces acting on the paraglider
The two forces acting on the paraglider in the vertical direction are:
- The lift force (L)
- The weight of the paraglider (W)

### Step 2: Determine the weight of the paraglider
Initially, the lift force is given as 1800 N, and it is stated that when the paraglider is in equilibrium (flying horizontally at constant speed), the lift force equals the weight of the paraglider. Therefore, we can conclude:
\[ W = L = 1800 \, \text{N} \]

### Step 3: Calculate the mass of the paraglider
Using the weight of the paraglider, we can find its mass (m) using the formula:
\[ W = m \cdot g \]
Where \( g \) (acceleration due to gravity) is approximately \( 9.8 \, \text{m/s}^2 \).
Rearranging the formula gives us:
\[ m = \frac{W}{g} = \frac{1800 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 183.67 \, \text{kg} \]

### Step 4: Analyze the new situation with the decreased lift force
When the lift force suddenly decreases to 1200 N, we need to find the net force acting on the paraglider:
- Upward force (Lift) = 1200 N
- Downward force (Weight) = 1800 N

The net force (F_net) can be calculated as:
\[ F_{\text{net}} = W - L = 1800 \, \text{N} - 1200 \, \text{N} = 600 \, \text{N} \]
This net force acts downward.

### Step 5: Calculate the vertical acceleration of the paraglider
Using Newton's second law, we can relate the net force to acceleration:
\[ F_{\text{net}} = m \cdot a \]
Rearranging gives us:
\[ a = \frac{F_{\text{net}}}{m} = \frac{600 \, \text{N}}{183.67 \, \text{kg}} \approx 3.26 \, \text{m/s}^2 \]

Since the net force is downward and we have taken the upward direction as positive, the acceleration will be negative:
\[ a \approx -3.26 \, \text{m/s}^2 \]

### Final Answer:
The vertical acceleration of the paraglider is approximately \( -3.26 \, \text{m/s}^2 \) (downward).

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