Question

Assuming birdman flies at a height of 78m, how fast should birdman fly to hit the bucket if the bucket is placed 75m from the start of the field?

Answer 1

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.