Answer:
I will suppose that:
The initial velocity of the birdman is horizontal.
Now, the only force acting on birdman will be the gravitational force, so we can write the acceleration of birdman as:
a(t) = -9.8m/s^2 (the negative sign is because this force is pulling downwards)
To get the vertical velocity, we can integrate over time and get:
v(t) = (-9.8m/s^2)*t + V0
where t represents the time in seconds, and V0 is the initial vertical velocity, i already assumed that the initial velocity is only horizontal, so here V0 = 0m/s.
v(t) = (-9.8m/s^2)*t
To find the vertical position as a function of time, we integrate again.
P(t) = (1/2)*(-9.8m/s^2)*t^2 + P0
Where P0 is the initial height, we know that it is 78m
Then the position is:
P(t) = (-4.9m/s^2)*t^2 + 78m.
Now, the bucket is placed in the ground, so he will reach the bucket when his vertical position is equal to zero, then we must solve:
P(t) = 0m = (-4.9m/s^2)*t^2 + 78m.
(4.9m/s^2)*t^2 = 78m.
t = √(78m/(4.9m/s^2)) = 3.99 seconds.
Now, in the horizontal plane, he must travel 75 meters in a time of 3.99 seconds if he wants to hit the bucket.
Now we can use the equation
Distance = Speed*Time
75m = S*3.99s
S = 75m/3.99s = 18.8 m/s.
So the horizontal speed is 18.8 m/s.
