You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are pointing the hose at the same angle and the distance the water reaches increases by a factor of 4, what fraction of the hose opening did you blocked?

Answer 1

since the range is proportional to the square of the initial velocity, if it has increased by a factor 4, the initial velocity has doubled.

Since the volume of water stays the same, that means that the area of the opening has been halved.

Answer 2

1/2