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a man weighing 700 n and a woman weighing 400 n have the same momentum. what is the ratio of the man's kinetic energy km to that of the woman kw ?

User Dillanm
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Since momentum is conserved, we can set the momentum of the man equal to the momentum of the woman:

p_man = p_woman

where p is the momentum, given by:

p = m * v

where m is the mass of the person, and v is their velocity.

Since the momentum is the same for both, we can write:

m_man * v_man = m_woman * v_woman

The kinetic energy of each person is given by:

K = 1/2 * m * v^2

where K is the kinetic energy, m is the mass, and v is the velocity.

The ratio of the man's kinetic energy to the woman's kinetic energy is:

K_man / K_woman = (1/2 * m_man * v_man^2) / (1/2 * m_woman * v_woman^2)

We can substitute the expression for the velocity in terms of the momentum, and simplify:

K_man / K_woman = (m_man / m_woman) * (v_man / v_woman)^2

K_man / K_woman = (m_man / m_woman) * (m_woman / m_man)^2

K_man / K_woman = m_woman^2 / m_man^2

Substituting the given values, we get:

K_man / K_woman = (400 N)^2 / (700 N)^2

K_man / K_woman = 0.102

Therefore, the ratio of the man's kinetic energy to the woman's kinetic energy is approximately 0.102.