Answer:
The estimated terminal velocity of the squirrel is approximately 7.74 m/s.
Step-by-step explanation:
To estimate the terminal velocity of the squirrel, we need to consider the forces acting on it during its fall. The two main forces involved are gravity and air resistance.
Let's calculate the gravitational force acting on the squirrel. The gravitational force can be calculated using the equation:
F_gravity = m * g
where m is the mass of the squirrel and g is the acceleration due to gravity (approximately 9.8 m/s²).
F_gravity = 0.555 kg * 9.8 m/s² = 5.4294 N
Next, let's consider the air resistance. The air resistance force can be approximated using the equation:
F_air = (1/2) * ρ * v² * A * C
where ρ is the air density (approximately 1.225 kg/m³), v is the velocity of the squirrel, A is the cross-sectional area, and C is the drag coefficient.
Given:
Cross-sectional area (A) = 11.5 cm * 23 cm = 264.5 cm² = 0.02645 m²
Surface area = 920 cm² = 0.092 m²
Drag coefficient for a horizontal skydiver = 0.7
Since the squirrel can be approximated as a rectangular prism, we'll use the surface area for the calculation.
Now, we can set up an equation to find the terminal velocity (v_terminal), where the air resistance force equals the gravitational force:
(1/2) * ρ * v_terminal² * A * C = m * g
Plugging in the known values:
(1/2) * 1.225 kg/m³ * v_terminal² * 0.092 m² * 0.7 = 0.555 kg * 9.8 m/s²
Simplifying the equation:
0.0906 * v_terminal² = 5.4294
v_terminal² = 5.4294 / 0.0906
v_terminal² = 59.879 m²/s²
v_terminal ≈ √(59.879) ≈ 7.74 m/s
Therefore, the estimated terminal velocity of the squirrel is approximately 7.74 m/s.