A baseball is hit with an initial velocity of 30 m/s at an angle of 40° with the horizontal displacement and the maximum height reached

[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To calculate the horizontal displacement and the maximum height reached by the baseball hit with an initial velocity of 30 m/s at an angle of 40°, we can break the problem down into two parts: horizontal motion and vertical motion. Break Down the Initial Velocity We will use trigonometry to find the horizontal and vertical components of the initial velocity ([tex]v_0[/tex]). Horizontal Component ([tex]v_{0x}[/tex]): [tex]v_{0x} = v_0 \cdot \cos(\theta)[/tex][tex]v_{0x} = 30 \cdot \cos(40^\circ)[/tex] Vertical Component ([tex]v_{0y}[/tex]): [tex]v_{0y} = v_0 \cdot \sin(\theta)[/tex][tex]v_{0y} = 30 \cdot \sin(40^\circ)[/tex] Calculate the Components Using the approximate values of cosine and sine: [tex]\cos(40^\circ) \approx 0.7660[/tex][tex]\sin(40^\circ) \approx 0.6428[/tex] Now we can calculate: Horizontal Component:[tex]v_{0x} \approx 30 \cdot 0.7660 \approx 22.98 \text{ m/s}[/tex] Vertical Component:[tex]v_{0y} \approx 30 \cdot 0.6428 \approx 19.28 \text{ m/s}[/tex] Calculate Maximum Height To find the maximum height (H), we use the formula: [tex]H = \frac{v_{0y}^2}{2g}[/tex] Where: [tex]g \approx 9.81 \text{ m/s}^2[/tex] (acceleration due to gravity) Calculating H: [tex]H = \frac{(19.28)^2}{2 \cdot 9.81} \approx \frac{370.49}{19.62} \approx 18.89 \text{ m}[/tex] Calculate Time of Flight The total time of flight (T) can be found using the formula: [tex]T = \frac{2v_{0y}}{g}[/tex] Calculating T: [tex]T = \frac{2 \cdot 19.28}{9.81} \approx \frac{38.56}{9.81} \approx 3.93 \text{ s}[/tex] Calculate Horizontal Displacement The horizontal displacement (R) is calculated using: [tex]R = v_{0x} \cdot T[/tex] Calculating R: [tex]R \approx 22.98 \cdot 3.93 \approx 90.31 \text{ m}[/tex] Conclusion Maximum Height Reached: Approximately 18.89 meters.Horizontal Displacement: Approximately 90.31 meters. [tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\begin{gathered} \boxed{\begin{array}{cc} \sf \footnotesize \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ···\: ʚ\: \: \: \: \: \: Hope\:it\:helps \: \: \: \: \: ɞ \:··· \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\footnotesize\:\# CarryOnLearning \\ \sf\footnotesize ૮₍´˶ \: • \: . \: • \: ⑅ ₎ა \: \leadsto \footnotesize\sf\color{purple} \underline{Study\:Well!}\end{array}}\end{gathered}[/tex][tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\large\qquad\qquad\qquad\tt MARCH/10/2025 [/tex]

Answered by chaser27 | 2025-03-10