Calculating the speed of a crane (using pythagoras) with different x & y speeds

In summary, the conversation discusses the use of Pythagorean theorem to calculate the time it takes for a crane to move diagonally in a steel processing warehouse simulation. The maximum speeds of the crane in the x and y directions are 40m/min and 12.5m/min respectively. The suggested method is to use t = d/v, where t is time, d is distance, and v is velocity. The resulting diagonal movement time is calculated to be 0.17 minutes, which is faster than the previous times calculated for movement in the x and y directions.
  • #1
Calico5
2
0
Hi,

Homework Statement



I'm designing a C++ program to simulate the operation of a steel processing warehouse. Part of my code requires me to calculate the time it takes for a crane to move certain distances (mainly diagonal ones) across a large shelving rack.

Homework Equations


The crane moves at different speeds in different directions.
Maximum x speed = 40m/min
Maximum y speed = 12.5m/min

I was thinking of using pythagoras theorem somehow to solves this (although its not required to be done this way) so:
c2 = a2 +b2

The Attempt at a Solution


I was thinking of using:

time = distance/speed

to calculate the time for each movement in x direction and y direction. Then using pythagoras theorem on the times to get the diagonal movement time. So an example would be:

14ybc5s.jpg


X-Time = 6/40 = 0.15min
Y-Time = 4/12.5 = 0.32min

Z-Time = SQRT(0.152+0.322) = 0.353min

Would that be correct? I am not sure if i can apply pythagoras theorem to time like that. Any Help is appreciated

Thanks
 
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  • #2
Calico5 said:
Hi,

Homework Statement



I'm designing a C++ program to simulate the operation of a steel processing warehouse. Part of my code requires me to calculate the time it takes for a crane to move certain distances (mainly diagonal ones) across a large shelving rack.

Homework Equations


The crane moves at different speeds in different directions.
Maximum x speed = 40m/min
Maximum y speed = 12.5m/min

I was thinking of using pythagoras theorem somehow to solves this (although its not required to be done this way) so:
c2 = a2 +b2

The Attempt at a Solution


I was thinking of using:

time = distance/speed

to calculate the time for each movement in x direction and y direction. Then using pythagoras theorem on the times to get the diagonal movement time. So an example would be:

14ybc5s.jpg


X-Time = 6/40 = 0.15min
Y-Time = 4/12.5 = 0.32min

Z-Time = SQRT(0.152+0.322) = 0.353min

Would that be correct? I am not sure if i can apply pythagoras theorem to time like that. Any Help is appreciated

Thanks


I would use Pythagorean theorem on the velocity and distance. Then use t = d/v. You would find how far the crane moves along the diagonal, and if the x-y speeds are constant, how fast it is moving along the diagonal so you could calculate the time.
 
  • #3
Thank you for the reply Apphysicist :)

Ahh right, i see. Tried out your method and got the following:

ZDistance = SQRT(42 + 62) = 7.211
ZSpeed = SQRT(402 + 12.52) = 41.907

t=d/v = 7.211/41.907 = 0.17min

That seems a bit quick doesn't it? given that the previous results were:
X-Time = 0.15min
Y-Time = 0.32min

i would have thought the pythagoras time would be closer to the slowest time. No?
 

1. How do you calculate the speed of a crane using Pythagoras?

The speed of a crane can be calculated using Pythagoras' theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the total speed of the crane, while the other two sides represent the x and y speeds. By using this formula, you can determine the total speed of the crane.

2. What are the x and y speeds of a crane?

The x and y speeds of a crane refer to the horizontal (x) and vertical (y) components of its movement. These speeds are measured in distance per unit of time, such as meters per second. By knowing both the x and y speeds, you can use Pythagoras' theorem to calculate the total speed of the crane.

3. Why is Pythagoras' theorem used to calculate the speed of a crane?

Pythagoras' theorem is used to calculate the speed of a crane because it is a mathematical formula that can be applied to right triangles, which represent the x and y components of the crane's movement. It allows us to find the total speed of the crane by taking into account both the horizontal and vertical speeds.

4. Can the speed of a crane change if the x and y speeds are different?

Yes, the speed of a crane can change if the x and y speeds are different. This is because the total speed of the crane is dependent on both the x and y components. If the x and y speeds are equal, the total speed of the crane will be the same as well. However, if the x and y speeds are different, the total speed will be a combination of these two speeds.

5. How is the speed of a crane with different x and y speeds represented visually?

The speed of a crane with different x and y speeds can be represented visually using a right triangle. The horizontal distance (x) is represented by the base of the triangle, while the vertical distance (y) is represented by the height of the triangle. The hypotenuse of the triangle represents the total speed of the crane, and its length can be found using Pythagoras' theorem.

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