Answer:
To estimate the terminal velocity of the squirrel, we need to consider the forces acting on it: its weight, the force of gravity, and the drag force. The terminal velocity is the velocity at which the sum of these forces is zero, meaning that the squirrel is no longer accelerating.
The weight of the squirrel is given by:
W = m * g
where m is the mass of the squirrel and g is the acceleration due to gravity (9.8 m/s^2).
The force of gravity is given by:
F_g = W
The drag force is given by:
F_d = (1/2) * C * rho * A * v^2
where C is the drag coefficient, rho is the density of air, A is the surface area of the squirrel, and v is its velocity.
The equation for terminal velocity can be written as:
0 = W - F_d
= m * g - (1/2) * C * rho * A * v^2
Solving for v, we get:
v = sqrt((2 * m * g) / (C * rho * A))
Plugging in the values for the squirrel, we get:
v = sqrt((2 * 560 g * 9.8 m/s^2) / (1.28 * 1.225 kg/m^3 * 144 cm^2))
= 15.4 m/s
Therefore, the terminal velocity of the squirrel is approximately 15.4 m/s.
To calculate the velocity of a person hitting the ground, we can use the same formula as above, but with the mass and surface area of the person.
Plugging in the values for the person, we get:
v = sqrt((2 * 56 kg * 9.8 m/s^2) / (1.28 * 1.225 kg/m^3 * 5000 cm^2))
= 51.5 m/s
Therefore, the velocity of the person hitting the ground would be approximately 51.5 m/s, assuming no drag contribution in such a short distance.