11 A . A baseball is thrown vertically into the air with a speed of \( 24.7 \mathrm{~m} / \mathrm{s} \). a) Draw a sketch of the scenario. b) How high does it go? c) What is the velocity at the top? d) How long does the round trip up and down require?

When a baseball is thrown vertically upwards with an initial speed, it experiences a deceleration due to gravity, which is approximately \(9.81 \, \mathrm{m/s^2}\) acting downwards. To find out how high it goes, we can use the formula \( h = \frac{v^2}{2g} \). Plugging in \( v = 24.7 \, \mathrm{m/s} \) and \( g = 9.81 \, \mathrm{m/s^2} \), we can calculate the height the baseball reaches. At the top of its flight, the velocity becomes \(0 \, \mathrm{m/s}\) before it starts descending back down. To find the total time for the round trip, we'll use the time to reach the peak, calculated with \( t = \frac{v}{g} \), and then double that for the entire journey. **Additional Information:** When the baseball reaches a height of approximately \( \frac{24.7^2}{2 \times 9.81} \approx 30.6 \, \text{meters} \), it's a perfect example of an inverted parabola motion. The maximum height is significant because this simple physics concept often appears in sports and engineering fields, showcasing the principles of kinematics. Don't forget to subtract minor errors due to air resistance in real-world scenarios! Beginners often mistake neglecting this factor, but it can be crucial for accurate predictions in fields like aerodynamics and ballistics. Always remember to apply the right physics principles while considering real-world dynamics!