Question

assuming birdman flies at a height of 82 m, how fast should birdman fly to hit the bucket if the bucket is placed 92 m from the start of the field?

Explanation:

Step1: Calculate time of fall

The vertical - motion of Birdman is a free - fall motion. The height \(h = 82m\), and the equation for vertical displacement in free - fall is \(h=v_{0y}t+\frac{1}{2}gt^{2}\). Since the initial vertical velocity \(v_{0y} = 0m/s\), the equation simplifies to \(h=\frac{1}{2}gt^{2}\), where \(g = 9.8m/s^{2}\). Solving for \(t\), we get \(t=\sqrt{\frac{2h}{g}}\).
\[t=\sqrt{\frac{2\times82}{9.8}}\]
\[t=\sqrt{\frac{164}{9.8}}\approx\sqrt{16.735}\approx 4.09s\]

Step2: Calculate horizontal velocity

The horizontal displacement \(x = 92m\), and the horizontal velocity \(v_x\) is constant (no horizontal acceleration, \(a_x=0\)). The equation for horizontal motion is \(x = v_x t\). Solving for \(v_x\), we get \(v_x=\frac{x}{t}\).
\[v_x=\frac{92}{4.09}\approx22.5m/s\]

Answer:

\(22.5m/s\)