A parachutist relies on air resistance mainly on her parachute to decrease her downward velocity. She and her parachutehave a mass of 55.0 kg and air

Result:
a) The weight of the parachutist is $55.0\text{kg}\times 9.8{\text{m/s}}^2$.
b) The free body diagram shows the weight ($\text{W}$) and the upward force due to air resistance (${\text{F}}_{\text{air}}$). The net force (${\text{F}}_{\text{net}}$) is the vector sum of these forces.
c) The acceleration of the parachutist is $\frac{{\text{F}}_{\text{net}}}{\text{mass}}$.
Solution:
a) The weight of an object can be calculated using the formula:
$\text{{Weight}\}=\text{{mass}\}\times \text{{acceleration due to gravity}\}$
Given that the mass of the parachutist and her parachute is 55.0 kg, and the acceleration due to gravity is approximately 9.8 m/s${}^2$, we can calculate the weight as follows:
$\text{{Weight}\}=55.0\text{kg}\times 9.8{\text{m/s}}^2$
b) A free body diagram shows all the forces acting on an object. In this case, the forces acting on the parachutist are the weight ($\text{W}$) and the upward force due to air resistance (${\text{F}}_{\text{air}}$). The net force (${\text{F}}_{\text{net}}$) is the vector sum of these forces. If the net force is positive, it means the overall force is upward; if it is negative, it means the overall force is downward.
c) The acceleration of the parachutist can be determined using Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
${\text{F}}_{\text{net}}=\text{mass}\times \text{acceleration}$
Since we know the net force acting on the parachutist (620 N) and the mass of the parachutist (55.0 kg), we can rearrange the equation to solve for the acceleration:
$\text{acceleration}=\frac{{\text{F}}_{\text{net}}}{\text{mass}}$

a) The weight of the parachutist can be calculated using the formula:
$\text{{Weight}\}=\text{{mass}\}\times \text{{acceleration due to gravity}\}$
Given that the mass of the parachutist is $55.0\text{kg}$ and the acceleration due to gravity is $9.8{\text{m/s}}^2$, we can substitute these values into the formula to find the weight:
$\text{{Weight}\}=55.0\text{kg}\times 9.8{\text{m/s}}^2=\boxed{539\text{N}}$
Therefore, the weight of the parachutist is $539\text{N}$.
b) The free body diagram for the parachutist can be represented as follows:
$\begin{array}{cccc}\hfill \text{Weight}\hfill & \hfill -\hfill & \hfill \text{Air Resistance}\hfill & \hfill =\text{Net Force}\hfill \\ \hfill \downarrow \hfill & \hfill \hfill & \hfill \uparrow \hfill & \hfill \hfill \\ \hfill \text{Downward}\hfill & \hfill \hfill & \hfill \text{Upward}\hfill & \hfill \hfill \\ \hfill \text{Force}\hfill & \hfill \hfill & \hfill \text{Force}\hfill & \hfill \hfill \end{array}$
The weight acts downward, while the air resistance exerts an upward force. The net force can be calculated by subtracting the air resistance force from the weight. Since the air resistance force is directed upward, the net force will be downward.
$\text{Net Force}=\text{Weight}-\text{Air Resistance}=539\text{N}-620\text{N}=\boxed{-81\text{N}}$
Therefore, the net force on the parachutist is $-81\text{N}$, which means it is directed downward.
c) The acceleration of the parachutist can be determined using Newton's second law:
$\text{Net Force}=\text{mass}\times \text{acceleration}$
Substituting the values we have, we can solve for the acceleration:
$-81\text{N}=55.0\text{kg}\times \text{acceleration}$
Dividing both sides by the mass:
$\text{acceleration}=\frac{-81\text{N}}{55.0\text{kg}}=\boxed{-1.47{\text{m/s}}^2}$
The acceleration of the parachutist is $-1.47{\text{m/s}}^2$, directed downward.

Step 1:
a) To find the weight of the parachutist, we can use the formula:
$\text{{Weight}\}=\text{{mass}\}\times \text{{acceleration due to gravity}\}$
Given that the mass of the parachutist is $m=55.0\text{{kg}\}$, and the acceleration due to gravity is approximately $9.8\text{{m/s}{\}}^2$, we can calculate the weight as follows:
$\text{{Weight}\}=55.0\text{{kg}\}\times 9.8\text{{m/s}{\}}^2=539\text{{N}\}$
Therefore, the weight of the parachutist is $539\text{{N}\}$.
Step 2:
b) The free body diagram for the parachutist will include two forces: the weight acting downward and the air resistance acting upward. Let's denote the weight as $W$ and the air resistance as $R$. The diagram can be represented as:
$\begin{array}{c}\hfill \uparrow \hfill \\ \hfill R\hfill \\ \hfill \uparrow \hfill \\ \hfill \text{{Parachutist}\}\hfill \\ \hfill \downarrow \hfill \\ \hfill W\hfill \end{array}$
The net force on the parachutist can be calculated by finding the vector sum of the forces. Since the air resistance is acting in the opposite direction to the weight, we subtract the magnitude of the air resistance from the magnitude of the weight to obtain the net force:
$\text{{Net Force}\}=W-R$
Substituting the values we know, the net force becomes:
$\text{{Net Force}\}=539\text{{N}\}-620\text{{N}\}=-81\text{{N}\}$
The net force is negative (-81 N), indicating that it is acting downward.
Step 3:
c) The acceleration of the parachutist can be determined using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
$\text{{Net Force}\}=m\times a$
Rearranging the equation to solve for acceleration gives:
$a=\frac{\text{Net Force}}{m}$
Substituting the known values:
$a=\frac{-81\text{N}}{55.0\text{kg}}\approx -1.47\text{{m/s}{\}}^2$
The acceleration of the parachutist is approximately $-1.47\text{{m/s}{\}}^2$, with the negative sign indicating that the acceleration is in the opposite direction to the chosen positive direction (downward in this case).