Final answer:
To hit the bucket placed 88 meters from the start of the field, Birdman should fly at a height of approximately 94.9 meters, assuming he is flying horizontally at a speed of 20 m/s and is influenced only by gravity.
Step-by-step explanation:
To calculate how high Birdman should fly to hit the bucket 88 meters away, we need to solve a projectile motion problem, assuming a constant horizontal velocity and the influence of gravity on the vertical motion.
To determine how high Birdman should fly, one would have to know the angle at which he is flying. However, because the angle is not provided, and if we assume Birdman launches himself horizontally at the beginning of the field, we can calculate the time it takes to reach the bucket by dividing the distance (88m) by the speed (20 m/s).
Time = Distance / Speed = 88m / 20 m/s = 4.4 s
Next, using the equation of motion under gravity, the height (h) Birdman should be at can be calculated assuming he drops under gravity for the time calculated:
h = 0.5 × g × t^2
Where g is the acceleration due to gravity (9.8 m/s^2) and t is the time in seconds.
h = 0.5 × 9.8 m/s^2 × (4.4 s)^2
h = 0.5 × 9.8 m/s^2 × 19.36 s^2 = 94.9 m
Therefore, Birdman should ideally start at a height of approximately 94.9 meters to hit the bucket if he flies horizontally at a speed of 20 m/s.