Two water jets are emerging from a vessel at a height of 50 centimeters and 100 centimeters. If their horizontal velocities at the point of ejection are 1 meter/second and 0.5 meters/second respectively, calculate the ratio of their horizontal distances of impact.
They both take the same amount of time to fall.
The first one has twice the speed so goes twice as far in that time.
1:04
4.2 meters/ second
To calculate the ratio of the horizontal distances of impact, we need to consider the horizontal motion of the water jets.
First, let's analyze the horizontal motion of the first water jet with an initial velocity of 1 meter/second. Since there is no acceleration acting horizontally (assuming no air resistance), the horizontal velocity remains constant throughout the motion. Therefore, the horizontal distance of impact can be calculated using the formula:
Distance = Velocity x Time
To find the time of flight, we need to consider the vertical motion of the water jet. The vertical motion can be analyzed separately for each jet.
For the water jet emerging from a height of 50 centimeters, we can use the formula for free fall motion in the vertical direction:
h = (1/2)gt^2
where h is the initial vertical height (in this case, 0.5 meters) and g is the acceleration due to gravity (approximately 9.8 meters/second^2).
Rearranging the formula to solve for time:
t = sqrt(2h/g)
For h = 0.5 meters, the time is approximately 0.32 seconds.
Now, we can calculate the horizontal distance traveled by the first water jet:
Distance1 = Velocity1 x Time
Substituting the values:
Distance1 = 1 meter/second x 0.32 seconds
Distance1 = 0.32 meters
Next, let's analyze the horizontal motion of the second water jet with an initial velocity of 0.5 meters/second. Following the same process as before, we find the time of flight for the water jet emerging from a height of 100 centimeters:
t = sqrt(2h/g)
For h = 1 meter, the time is approximately 0.45 seconds.
Now, we can calculate the horizontal distance traveled by the second water jet:
Distance2 = Velocity2 x Time
Substituting the values:
Distance2 = 0.5 meter/second x 0.45 seconds
Distance2 = 0.225 meters
Finally, to find the ratio of the horizontal distances of impact:
Ratio = Distance1 / Distance2
Ratio ≈ 0.32 meters / 0.225 meters
Ratio ≈ 1.42
Therefore, the ratio of the horizontal distances of impact is approximately 1.42.