Yes, if we know the Earth's mass
Explanation:
The momentum of an object is a vector quantity given by the equation

where
m is the mass of the object
v is its velocity
In this case, we are asked if we can find the velocity of the Earth by starting from its momentum. Indeed, we can. In fact, we can rewrite the equation above as

Therefore, if we know the momentum of the Earth (p) and we know its mass as well (m), we can solve the formula to find the Earth's velocity.
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We don't know anything about the amount of distance it travels, but that's okay. The only equation we need here is
velocity(final) = velocity(initial) + acceleration * time
vf = vi + (a * t)
The ball is dropped from rest, so vi = 0 m/s.
We want it so that the ball hits the ground with a final velocity of 60 m/s, so vf = 60 m/s.
We are given the acceleration due to gravity, a = 9.8 m/s^2.
We are solving for the time, t = ?.
Now we just plug in the values.
vf = vi + (a * t)
60 m/s = 0 m/s + (9.8 m/s^2)*(t)
60 = 9.8t
60 / 9.8 = t
t = 6.122 s
Hopefully this is the right answer.
When is at the end of the runway the velocity of the plane is given by the equation

where s=1800 m is the runway length. Thus
At half runway the velocity of the plane is

Therefore at midpoint of runway the percentage of takeoff velocity is
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