The answer is: 1 km
If the size is small than 1km in diameter, the object would be classified as a a meteoroid, not an asteroid. Up until the year of 2018, NASA has spotted around 147,132 asteroids. From that number, around 8% of them had the risk of colliding with the earths.
For this we will use kinematic equations.
We need the time of flight to compute the range.
With the given information, the most useful formula is:
Δy=v0yt−g2t2
Because our equation is taking only vertical motion into account,
v0y=30sin(45)
Because we are looking for the range of the object,
Δy=0
This leaves us with only one unknown: t
0=30sin(45)t−g2t2
g2t2=30sin(45)t
g2t=30sin(45)
t=60gsin(45)
For horizontal distance, the formula we need is:
Δx=v0xt
Because we are taking into account the horizontal range,
v0x=30cos(45)
In substituting our derived values into the equation we can see that:
Δx=30cos(45)∗60gsin(45)
Range=30cos(45)∗60gsin(45)
Renewable.
hope this helps.
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