Question

assuming birdman flies at a height of 58 m, how fast should birdman fly to hit the bucket if the bucket is placed 71 m from the start of the field? scoreboard horizontal distance (dx) horizontal velocity (vx) height: 0 m/s check answer

Explanation:

Step1: Calculate time of fall

The vertical - motion is a free - fall motion. The height $h = 58$ m, and the equation for vertical displacement in free - fall is $h=v_{0y}t+\frac{1}{2}gt^{2}$. Since the initial vertical velocity $v_{0y} = 0$ m/s, the equation simplifies to $h=\frac{1}{2}gt^{2}$. Solving for $t$, we get $t=\sqrt{\frac{2h}{g}}$. Given $g = 9.8$ m/s² and $h = 58$ m, $t=\sqrt{\frac{2\times58}{9.8}}\approx\sqrt{\frac{116}{9.8}}\approx\sqrt{11.84}\approx3.44$ s.

Step2: Calculate horizontal velocity

The horizontal distance $d_x=71$ m. In horizontal motion (with no acceleration, $a_x = 0$), the equation is $d_x=v_x t$. Solving for $v_x$, we have $v_x=\frac{d_x}{t}$. Substituting $d_x = 71$ m and $t\approx3.44$ s, $v_x=\frac{71}{3.44}\approx20.64$ m/s.

Answer:

20.64 m/s