Baseball Mass
1. **State the problem:** We are given the kinetic energy (KE) of a baseball as 160 J and its speed as 169.1 km/h. We need to find the mass of the baseball in grams (g).
2. **Convert speed to meters per second (m/s):**
$$169.1\ \text{km/h} = 169.1 \times \frac{1000}{3600} = 46.9722\ \text{m/s}$$
3. **Recall the kinetic energy formula:**
$$KE = \frac{1}{2} m v^2$$
where $m$ is mass in kilograms and $v$ is velocity in m/s.
4. **Rearrange the formula to solve for mass $m$:**
$$m = \frac{2 KE}{v^2}$$
5. **Substitute the known values:**
$$m = \frac{2 \times 160}{(46.9722)^2} = \frac{320}{2205.6} \approx 0.1451\ \text{kg}$$
6. **Convert mass from kilograms to grams:**
$$0.1451\ \text{kg} = 0.1451 \times 1000 = 145.10\ \text{g}$$
**Final answer:** The mass of the baseball is approximately **145.10 g**.