Question

A 575 g squirrel with a frontal surface area of 0.0146 m^2 falls from a 8.5 m tree to the ground. Assume the density of air in this problem is given by 1.21 kg/m^3. (a) What is its terminal velocity in m/s? (Use a drag coefficient of 0.70 and assume down is positive) (b) What will the velocity (in m/s) of a 56 kg person falling that distance, assuming no drag contribution?

Answer 1

Answer:

a) 30.20 m/s

b) 12.91 m/s

Explanation:

Mass of squirrel = 575 g = m

Drag coefficient = 0.70 = C

Density of air = 1.21 kg/m³ = ρ

frontal surface area = 0.0146 m² = A

Height the squirrel falls = 8.5 m = h

a) Drag force

$F=\frac{1}{2}Av^2C\rho\\\Rightarrow F=\frac{1}{2}0.0146v^2\times 0.7\times 1.21$

This force will oppose gravity

$mg=F\\\Rightarrow 0.575\times 9.81=\frac{1}{2}0.0146v^2\times 0.7\times 1.21^2\\\Rightarrow \frac{0.575\times 9.81\times 2}{0.0146\times 0.7\times 1.21}=v^2\\\Rightarrow v=30.20\ m/s$

∴ Terminal velocity is 30.20 m/s

b) Neglecting drag force we get

$mgh=\frac{1}{2}mv^2\\\Rightarrow v=\sqrt{2gh}\\\Rightarrow v=\sqrt{2\times 9.81\times 8.5}\\\Rightarrow v=12.91\ m/s$

∴ Velocity of a 56 kg person falling that distance, assuming no drag contribution is 12.91 m/s