The speed of how fast the birdman should be to hit the bucket is 18.8 m/s
The only force acting on the height at which birdman flies is the gravitational force field.
Suppose the initial velocity (u) is parallel to the ground when the time (t) hits the ground.
Then, we can use the second equation of motion to determine the time (t) when the bird hits the ground.
[tex]\mathbf{S = ut + \dfrac{1}{2}gt^2}[/tex]
[tex]\mathbf{78 \ m =(0)t + \dfrac{1}{2}(9.8)t^2}[/tex]
[tex]\mathbf{78 \ m =4.9 t^2}[/tex]
[tex]\mathbf{t^2 = \dfrac{78 \ m}{4.9 m/s^2} }[/tex]
[tex]\mathbf{t^2 = 15.918 \ s^2}[/tex]
[tex]\mathbf{t =\sqrt{ 15.918 \ s}}[/tex]
[tex]\mathbf{t =3.989\ s}}[/tex]
Now, the speed of how fast the birdman should be to hit the bucket can be determined using;
[tex]\mathbf{Speed = \dfrac{Distance}{Time}}[/tex]
[tex]\mathbf{Speed = \dfrac{75 \ m }{3.989\ s}}[/tex]
[tex]\mathbf{Speed = 18.8 m/s}[/tex]
Therefore, we can conclude that the speed of how fast the birdman should be to hit the bucket is 18.8 m/s
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