Part A:

A cardinal (Richmondena cardinalis) of mass 4.50×10^−2 kg and a baseball of mass 0.142 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude p(c) of momentum to the magnitude p(b) of the baseball's momentum?

Part B:
A man weighing 650 N and a woman weighing 460 N have the same momentum. What is the ratio of the man's kinetic energy K(m) to that of the woman K(w)?

(A)

KE₁=m₁v₁²/2= (m₁v₁)²/2 m₁=p₁²/2m₁
KE₂=m₂v₂²/2= (m₂v₂)²/2 m₂= p₂²/2m₂
KE₁=KE₂
p₁²/2m₁=p₂²/2m₂
p₁²/p₂²=m₁/m₂
p₁/p₂=sqrt(m₁/m₂)
(B)
KE₁= p₁²/2m₁
KE₂= p₂²/2m₂
KE₁/KE₂=m₂/m₁

Part A: To find the ratio of the cardinal's momentum to the baseball's momentum, we can use the formula for momentum:

Momentum (p) = mass (m) × velocity (v)

Since the kinetic energy of the cardinal and the baseball is the same, we can equate their kinetic energy formulas:

0.5 × m(c) × v(c)^2 = 0.5 × m(b) × v(b)^2

Since the masses of the cardinal (m(c)) and the baseball (m(b)) are given, we can solve for the ratio of their momentum:

p(c) / p(b) = (m(c) × v(c)) / (m(b) × v(b))

To find the ratio of momentum, we need to find the velocities of the cardinal and the baseball.

Knowing the mass and kinetic energy, we can find the velocity using the formula:

Kinetic energy (KE) = 0.5 × mass × velocity^2

For the cardinal:

0.5 × m(c) × v(c)^2 = KE
0.5 × (4.50×10^-2 kg) × v(c)^2 = KE

For the baseball:

0.5 × m(b) × v(b)^2 = KE
0.5 × (0.142 kg) × v(b)^2 = KE

Using the given data, solve for the velocities v(c) and v(b). Then substitute the velocities into the momentum ratio equation to find p(c) / p(b).

Part B: To find the ratio of the man's kinetic energy to that of the woman, we need to relate their kinetic energy and momentum.

First, let's understand the relationship between momentum and kinetic energy:

Momentum (p) = mass (m) × velocity (v)
Kinetic energy (KE) = 0.5 × mass × velocity^2

In the given scenario, both the man and the woman have the same momentum. Therefore, we can equate their momentum formulas:

m(m) × v(m) = m(w) × v(w)

Since the weights of the man (650 N) and the woman (460 N) are given, we can use the equation:

Weight (W) = mass (m) × gravity (g)

So we have:

m(m) × g = 650 N
m(w) × g = 460 N

Dividing the two equations, we can find the mass ratio:

(m(m) / m(w)) = (650 N) / (460 N)

Now that we have the mass ratio, we can use it to find the ratio of kinetic energy:

K(m) / K(w) = (0.5 × m(m) × v(m)^2) / (0.5 × m(w) × v(w)^2)

To solve for the velocities v(m) and v(w), we need additional information such as the distance traveled or the time taken.