To solve for the velocity of the pitcher, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant if no external forces are acting on it.
We can express this mathematically as follows:
\[ \text{Initial Momentum} = \text{Final Momentum} \]
Initially, both the pitcher and the baseball are at rest, so the initial momentum is zero. Therefore, we can set up the equation based on their final momenta when the baseball is thrown.
Let:
- \( m_p = \) mass of the pitcher = 50 kg,
- \( v_p = \) velocity of the pitcher (which we want to find),
- \( m_b = \) mass of the baseball = 0.15 kg,
- \( v_b = \) velocity of the baseball = 35 m/s.
According to conservation of momentum:
\[ 0 = m_p \cdot v_p + m_b \cdot v_b \]
We can rearrange this equation to solve for the velocity of the pitcher:
\[ m_p \cdot v_p = - m_b \cdot v_b \]
Substituting the given values into the equation:
\[ 50 \cdot v_p = - (0.15) \cdot (35) \]
Calculating the right side:
\[ 50 \cdot v_p = - 5.25 \]
Now we can solve for \( v_p \):
\[ v_p = \frac{-5.25}{50} \]
\[ v_p = -0.105 , \text{m/s} \]
Rounding this to one decimal place, we find:
\[ v_p \approx -0.1 , \text{m/s} \]
Thus, the velocity of the pitcher is approximately \(-0.1 , \text{m/s}\). Therefore, the answer is:
\(\text{−0.1 m/s}\)
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