Given:
Initial velocity, \(v_1 = 19.04 \, m/s\)
Final velocity, \(v_2 = 17.14 \, m/s\)
Mass of the ball, \(m = 0.310 \, kg\)
Impulse, \(I = m(v_2 - v_1)\)
Substitute the values:
\(I = 0.310 \times (17.14 - 19.04)\)
\(I = 0.310 \times (-1.90)\)
\(I = -0.589 \, kg
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