a baseball player friend of yours wants to determine his pitching speed. you have him stand on a ledge and…

Explanation:

Step1: Analyze vertical - motion

The ball is in free - fall vertically. The initial vertical velocity $v_{0y}=0$ m/s, the vertical displacement $y = - 9.0$ m (taking downwards as negative), and the acceleration $a=-g=- 9.8$ m/s². Use the equation $y = v_{0y}t+\frac{1}{2}at^{2}$. Since $v_{0y} = 0$ m/s, the equation simplifies to $y=\frac{1}{2}at^{2}$. $$y=\frac{1}{2}at^{2}\Rightarrow t=\sqrt{\frac{-2y}{g}}$$

Step2: Calculate the time of flight

Substitute $y=-9.0$ m and $g = 9.8$ m/s² into the formula for $t$. $$t=\sqrt{\frac{-2\times(-9.0)}{9.8}}\text{ s}\approx\sqrt{\frac{18}{9.8}}\text{ s}\approx1.355\text{ s}$$

Step3: Analyze horizontal - motion

In the horizontal direction, there is no acceleration ($a_x = 0$ m/s²), and the horizontal displacement $x = 30$ m. The horizontal velocity (pitching speed) $v_{0x}$ is constant. Use the equation $x = v_{0x}t$. Then $v_{0x}=\frac{x}{t}$.

Step4: Calculate the pitching speed

Substitute $x = 30$ m and $t\approx1.355$ s into the formula for $v_{0x}$. $$v_{0x}=\frac{30}{1.355}\text{ m/s}\approx22.1\text{ m/s}$$

Answer:

22.1 m/s