Comparison of the range:
If a second projectile is launched with half of the initial velocity of the first projectile. The range of the second projectile is one-fourth of the first one.
Calculation:
Step-1:
It is given that the first particle has an initial velocity of
, and the second particle has an initial velocity of
. It is required to compare the range of the second projectile with the first one.
It is known that the range of a projectile is calculated as,

Where u is the initial speed, g is the acceleration due to gravity, and
is the angle at which the particle is thrown.
This problem
is the same in both cases.
Step-2:
Therefore the range of the first projectile is,

The range of the second projectile is,

Therefore,

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