A 3.000 kg ball is pitched with a kinetic energy of 20.00 J . The magnitude of the momentum of the ball is

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1. The kinetic energy of the ball is given by
   $$
   KE = \frac{1}{2} m v^2.
   $$
   Here, $$ KE = 20.00 \, \text{J} $$ and $$ m = 3.000 \, \text{kg} $$.

2. Solve for the speed $$ v $$:
   $$
   \frac{1}{2} m v^2 = 20.00.
   $$
   Multiply both sides by 2:
   $$
   m v^2 = 40.00.
   $$
   Now, substitute $$ m = 3.000 \, \text{kg} $$:
   $$
   3.000 \, v^2 = 40.00.
   $$
   Divide by 3.000:
   $$
   v^2 = \frac{40.00}{3.000} \approx 13.3333.
   $$
   Taking the square root:
   $$
   v \approx \sqrt{13.3333} \approx 3.6515 \, \text{m/s}.
   $$

3. The momentum $$ p $$ is given by
   $$
   p = m v.
   $$
   Substitute the values:
   $$
   p = 3.000 \, \text{kg} \times 3.6515 \, \text{m/s} \approx 10.9545 \, \text{kg} \cdot \text{m/s}.
   $$

4. Rounding to an appropriate number of significant figures, the magnitude of the momentum is approximately
   $$
   10.95 \, \text{kg} \cdot \text{m/s}.
   $$
The magnitude of the ball's momentum is approximately 10.95 kg·m/s.

A 3.000 kg ball is pitched with a kinetic energy of 20.00 J . The magnitude of the momentum of the ball is

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