Final answer:
To hit the bucket, Birdman needs to calculate the correct horizontal velocity and the appropriate vertical velocity to rise to the height of the bucket. The problem requires solving a quadratic equation to find the value of the horizontal velocity. However, the exact values of the velocities required to hit the bucket are not given in the question.
Step-by-step explanation:
To calculate the speed at which Birdman should fly to hit the bucket, we can use the principles of projectile motion. Since Birdman is flying horizontally, only the vertical motion needs to be considered. We can use the equation:
dx = vx * t
Where dx is the horizontal distance, vx is the horizontal velocity, and t is the time of flight. We also have the equation:
h = vy * t - 0.5 * g * t2
Where h is the height, vy is the vertical velocity, and g is the acceleration due to gravity. We can solve these equations simultaneously:
86 = vx * t
89 = vy * t - 0.5 * 9.8 * t2
By substituting t = 86/vx into the second equation, we can simplify it to:
89 = (89/vx) * (86/vx) - 0.5 * 9.8 * (86/vx)2
Simplifying further gives us a quadratic equation:
0.5 * 9.8 * (86/vx)2 - (89/vx) * (86/vx) + 89 = 0
We can solve this equation to find the value of vx. However, the specific values of vx and vy required to hit the bucket will depend on the specific target distance and height, which are not provided in the question.