Help needed with a question of POWER(physics)?

Messy to explain, but here goes.

Some background you need to know...

When you throw something vertically up, at half the max. height, half the energy is potential and half is kinetic. That means the kinetic energy is half its initial value.

Since kinetic energy is proportional to v², v² has been halved, so v is reduced by √2.
_____

In this question the force is weight (mg). It acts vertically down so we only consider the vertical component of motion. The horizontal component makes no difference.
_____

Power = force x velocity (P = Fv)

For an object in free-fall, the force is the weight (mg). So the power dleivered by gravity is P = mgv.
________________________________________

The initial vertical component of velocity = usinθ.

At half max height the velocity = usinθ/√2

Power = force x velocity.
P = Fv
. . = mg usinθ/√2

So answer 2) is correct.

Now the tricky bit.

Power is delivered by gravity when the object is falling (increasing the object's kinetic energy and speeding it up). Power has a positive value.

But we can say 'negative power' is delivered by gravity when the object is rising. This means energy is being removed fromthe object - kinetic energy is decreasing as the object is beng slowed down. P is negative.

Note that cos(90° + θ) = -sinθ
So [answer 3)] = -[answer 2)]

So both 2) and 3) are correct. Answer 2) is a positive value for the falling mass; answer 3) is a negative value for the rising mass.

So answer 4) is correct.

for a projectile, at half of maximum height, the speed will be ' u sin(theta)/square root(2).
so that the gravitation power of the body will be power = force x velocity
ie., power = mg x u sin(theta) / square root(2), hence the correct answer is (2), and this is same as (3) as well. so correct choice is (4)