4) a 560 - g squirrel with a surface area of 930cm² falls from a 5.0 - m tree to the ground. estimate its…
4) a 560 - g squirrel with a surface area of 930cm² falls from a 5.0 - m tree to the ground. estimate its terminal velocity. (use a drag coefficient for a horizontal skydiver.) what will be the velocity of a 56 - kg person hitting the ground, assuming no drag contribution in such a short distance?
Answer
Explanation:
Step1: Recall the formula for terminal velocity
The formula for terminal velocity $v_t=\sqrt{\frac{2mg}{C\rho A}}$, where $m$ is the mass, $g = 9.8\ m/s^{2}$ is the acceleration due to gravity, $C$ is the drag - coefficient, $\rho$ is the density of air ($\rho= 1.29\ kg/m^{3}$ for air near the surface of the Earth), and $A$ is the surface area. For a horizontal skydiver, the drag - coefficient $C\approx1$.
Step2: Convert the mass and area to SI units
The mass of the squirrel $m = 560\ g=0.56\ kg$, and the surface area $A = 93.0\ cm^{2}=93.0\times10^{- 4}\ m^{2}$.
Step3: Substitute the values into the terminal - velocity formula
[ \begin{align*} v_t&=\sqrt{\frac{2mg}{C\rho A}}\ &=\sqrt{\frac{2\times0.56\times9.8}{1\times1.29\times93.0\times10^{-4}}}\ &=\sqrt{\frac{10.976}{0.12057}}\ &=\sqrt{91.0344}\ &\approx9.54\ m/s \end{align*} ]
Answer:
The terminal velocity of the squirrel is approximately $9.54\ m/s$.