In this problem, use the exact values you enter in previous answer(s) to make later calculation(s).

We develop an empirical formula connecting the wingspan and the mass of some species able to fly. Then we evaluate a few interesting consequences. (The first to make these considerations was Leonardo da Vinci.)

If the density of all mammals is approximately the same as the density of water, what is the ratio of the volume of a hackney pony to the volume of a sheep? (Use data from this table as necessary.)

Vhackney pony

Vsheep

 =

What is the ratio of the volume of a porcupine to the volume of a brown lemming?

Vporcupine

Vbrown lemming

 =

Could 2 of every modern land mammal on this table be housed in an ark that is 300 cubits long, 50 cubits wide, and 30 cubits in height? (Assume 1 cubit is approximately 45 cm.)
Could 2 of every modern land mammal on this table be housed in the volume equivalent to that of a blue whale?

The figure below shows a back view of an adult male and an adult female human (accompanied by two children). (Assume that to the right and up are the positive x and y directions.)

In the figure below, assume

m₁ = 10 kg

and

m₂ = 5.1 kg.

The coefficient of static friction between the object on the table and the table surface is 0.8 and the coefficient of kinetic friction is 0.4. The system is set in motion with the object of mass m₂ moving downward. What is the acceleration of the object of mass m₁?

magnitude	m/s2
direction	---Select--- to the left to the right The magnitude is zero.

Two objects, each moving with the same speed but in opposite directions, collide head-on. After the collision, the smaller object of mass

m = 225 g

is embedded in the larger object of mass

M = 560 g.

Find an expression for the final speed in terms of the initial speed. (Use the following as necessary: v_i for the initial speed)

v_f =

Some birds of prey, such as the northern goshawk, hunt other birds in midair. Typically, the hawk spots the prey while soaring high above, then dives in for the kill with the deadly grip of its talons. They do not shy away from larger prey, such as ducks and crows. Using the change in linear momentum, we want to estimate the impact on the hawk when completing a successful kill by clawing into the prey, which we take to be an unsuspecting American crow. Use mass of crow

m_C = 455 g,

horizontal flight of the crow with speed

v_C = 11 m/s,

mass of hawk

m_H = 901 g,

flight path in the same plane as the crow but approaching from behind with

v_H = 23 m/s

and with an angle of

θ = 74°

with the horizontal, as illustrated in the side view of the figure below.

A standard man holds an object of mass

m = 4 kg

on the palm of the hand with the arm stretched, as shown in the figure below.

A standard man uses a bicycle of mass 28 kg to travel at constant speed along a 4 km long road up a hill. The hilltop is 240 m above the point of departure and the standard man needs ½ hour for the trip.

A second standard man chooses to climb the hill along the shortest route, a trail of 3 km length. If this standard man uses the same power, will he reach the hilltop before, after, or together with the standard man taking the longer route? (Assume this second standard man is also using a bicycle of mass 28 kg and both standard men depart at the same time.)