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?
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.
1/2
To solve this problem, let's assume that the original distance the water reaches without blocking the hose opening is represented by "D" and the distance the water reaches with your finger blocking a fraction of the hose opening is represented by "4D". We want to find the fraction of the hose opening that you blocked.
Since the water reaches four times the original distance, we can set up the following equation:
4D = D + Blocked distance
Where "Blocked distance" represents the distance that is blocked by your finger. Rearranging the equation, we get:
3D = Blocked distance
This means that the distance blocked is three times the original distance (D). To find the fraction of the hose opening that was blocked, we can divide the blocked distance by the total distance the opening spans. The fraction is given by:
Fraction blocked = Blocked distance / Total distance
Since the total distance the opening spans is equal to D, the fraction blocked is:
Fraction blocked = 3D / D = 3/1 = 3/1 = 3
Therefore, you blocked 3/4 (or 3/1) of the hose opening.
To solve this problem, let's assume that without blocking the hose opening, the water reaches a distance of "x" units. When you block the hose opening partially with your finger, the water reaches a distance of "4x" units.
Now, let's consider the ratio of the distances reached with and without blocking the hose opening:
(With blocking) / (Without blocking) = 4x / x = 4
So, the water reaches a distance four times greater when you block the hose opening.
To determine the fraction of the hose opening you blocked, we need to find the difference between the two distances:
Blocked distance = 4x - x = 3x
Therefore, you blocked 3x units of distance.
To find the fraction of the hose opening you blocked, divide the blocked distance by the original distance:
Fraction blocked = Blocked distance / Original distance = 3x / x = 3
So, you blocked 3/1 or simply 3/3 of the hose opening.
Therefore, you blocked 1/3 (one-third) of the hose opening.