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dramadeur
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I don't quite get, where does the V0x=v * d/(sqrt(d^2+(h-y0)^2) come from?
also, what does (h-y0) equal to? t/v0y?
Dart Trajectory: V0x Calculation Explained
- Thread starter dramadeur
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In summary, the equation V0x=v * d/(sqrt(d^2+(h-y0)^2) comes from the Pythagorean theorem, where the velocity v is split into horizontal and vertical components. The ratio of these components is equal to the ratio of the horizontal and vertical lengths of a triangle in the diagram to the length of the hypotenuse. (h-y0) represents the difference in two heights and is a constant in the equation. It can also be expressed as t/v0y at a particular time.
I don't quite get, where does the V0x=v * d/(sqrt(d^2+(h-y0)^2) come from?
also, what does (h-y0) equal to? t/v0y?
- #2
PeterDonis
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dramadeur said:
It's the Pythagorean theorem; the velocity ##v## is being split up into its horizontal and vertical components. The ratio of the components will be the same as the ratio of the horizontal and vertical lengths of the triangle in the diagram to the length of the hypotenuse.
- #3
PeterDonis
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dramadeur said:
At a particular time ##t##, yes. But that's because ##t## changes, not because ##h - y_0## changes. ##h - y_0## is a constant and is taken straight off the diagram; it's just the difference in two heights (which means it's the vertical side of the triangle I referred to in my previous post).
1. What is V0x and why is it important in calculating dart trajectory?
V0x, also known as initial horizontal velocity, is the initial velocity of a dart in the horizontal direction. It is important in calculating dart trajectory because it determines the distance the dart will travel in the x-axis.
2. How is V0x calculated?
V0x can be calculated by multiplying the initial velocity of the dart by the cosine of the launch angle.
3. How does V0x affect the trajectory of a dart?
V0x affects the trajectory of a dart by determining the distance it will travel in the x-axis. A higher V0x will result in a longer horizontal distance, while a lower V0x will result in a shorter distance.
4. Can V0x be changed during the flight of a dart?
No, V0x cannot be changed during the flight of a dart. It is a constant value determined by the initial conditions of the dart, such as the thrower's arm speed and angle of release.
5. Are there any other factors that can affect dart trajectory besides V0x?
Yes, there are other factors that can affect dart trajectory, such as air resistance, wind speed and direction, and the weight and shape of the dart. These factors can alter the path of the dart and should be taken into consideration when calculating its trajectory.
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