Question

assuming birdman flies at a speed of 36 m/s, how high should birdman fly to hit the bucket if the bucket is placed 134 m from the start of the field?

Explanation:

Step1: Calculate the time of flight

In the horizontal - direction, the motion is a uniform - motion. The formula for horizontal motion is $dx = vx\times t$. We know that $dx = 134$ m and $vx = 36$ m/s. So, $t=\frac{dx}{vx}$.
$t=\frac{134}{36}\text{ s}\approx3.72$ s

Step2: Calculate the height

In the vertical - direction, the motion is a free - fall motion. The initial vertical velocity $vy_0 = 0$ m/s, and the acceleration due to gravity $g = 9.8$ m/s². The formula for vertical displacement is $h=vy_0t+\frac{1}{2}gt^{2}$. Since $vy_0 = 0$ m/s, $h=\frac{1}{2}gt^{2}$.
Substitute $t=\frac{134}{36}$ s and $g = 9.8$ m/s² into the formula:
$h=\frac{1}{2}\times9.8\times(\frac{134}{36})^{2}$
$h = 67.7$ m

Answer:

67.7 m