An outdoor Wi-Fi unit for a picnic area has a 130 mW output and a range of about 50 m. What output power (in mW) would reduce its range to 14 m for use with the same devices as before

the angular speed of the stone at the moment of release is 15.05 rad/s

Explanation:

Given the data in the question;

The point of release ( height ) h = 25.6 m

the time of the fall of the stone will be;

⇒√( 2h/g )

we know that g = 9.81 m/s

so we substitute

t = √( (2 × 25.6 m) / 9.81 m/s )

t = √( 51.2 / 9.81 m/s )

t = √( 5.219164 s )

t = 2.285 s

Now, let v represent velocity at the time of release

them v × t ~ v × 2.285 s is the horizontal distance traveled.

Given that; The horizontal distance of point X from the base of the cliff (directly beneath the point of release) is 34.4 times the radius of the circle.

so

v × 2.285 = 34.4 × radius

Now, if the angular speed is ω then velocity at the time of release will be;

v = radius × ω

hence;

(radius × ω)  × 2.285 = 34.4 × radius

radius cancels each other out and we have;

ω  × 2.285 = 34.4

ω = 34.4 / 2.285

ω = 15.05 rad/s

Therefore, the angular speed of the stone at the moment of release is 15.05 rad/s