Would a 35 g mouse (Body length = 4 cm) die if it jumped a distance of 1.2 km into the grand canyon?

Would a 35 g mouse (Body length = 4 cm) die if it jumped a distance of 1.2 km into the grand canyon? Perform a calculation that demonstrates your answer. Model the body of the mouse as a sphere and assume that the mouse would die if it hit the ground at a speed greater than 50 m/s.

Answer The mouse survives the fall because the terminal velocity of 32.4 m/s is less than the deadly velocity.

In order to gain full credit, you need to show your work, including a listing of (1) the governing equations, (2) all parameters and variables, (3) all necessary assumptions, (4) the steps to finding the solution, with a descriptive sentence.

Parameter Symbol Value Units

Density of air ρ 1.2 kg/m3

Density of water ρ 1,000 kg/m3

Density of mineral oil ρ 880 kg/m3

Dynamic viscosity of air µ 1.81E-5 Pa s

Dynamic viscosity of water µ 8.90E-4 Pa s

Dynamic viscosity of mineral oil µ 0.1012 Pa s

Drag coefficient for a sphere (Re>1000) Cd 0.4

Drag coefficient for a fish or squid (Re>1000) Cd 0.006