Calculating Projectile Distance: A Theme Park Curiosity

In summary, a user is looking to calculate the possible distance traveled by a projectile from a set height, speed, and release angle for a new ride at their local theme park. The given parameters include a release height of 121.92 meters, a projectile mass of 90.72 kg, a radius of 6.01 meters, a velocity of 15.65 m/s, a centripetal force of 3697.07 N, and an angle of release of 45°. The discussion also considers the calculations for initial vertical and horizontal velocities, the time at which the vertical velocity reaches 0, the height at this point, the time to fall down from this height, and the total flight time for calculating the
  • #1
shini
2
0
Was not sure where to post this specifically, but I am looking to calculate the possible distance traveled by by a projectile from a set height, speed, and release. Its just curiosity from seeing a new ride being brought to my local theme park.

Height of release is 121.92 meters.
Mass of projectile is 90.72 kg.
Radius is 6.01 meters.
Velocity is 15.65 m/s.
Centripetal force is 3697.07 N.
Angle of release is 45°.

Thanks for any input on this.
 
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  • #2


shini said:
Was not sure where to post this specifically, but I am looking to calculate the possible distance traveled by by a projectile from a set height, speed, and release. Its just curiosity from seeing a new ride being brought to my local theme park.

Height of release is 121.92 meters.
Mass of projectile is 90.72 kg.
Radius is 6.01 meters.
Velocity is 15.65 m/s.
Centripetal force is 3697.07 N.
Angle of release is 45°.

Thanks for any input on this.

Welcome to the PF.

How did you get that centripital force? Do you have any pics of the ride?
 
  • #3


Neglecting air resistance (a good idea if you do not want to simulate it), you do not need any parameters apart from the initial velocity and the angle. The device to accelerate the object does not matter.

Can you calculate the initial vertical and horizontal velocity?
Based on this, can you calculate the time at which the vertical velocity gets 0?
Can you calculate the height at this point?
Can you calculate the time to fall down, if you know this height?
If you know the total flight time, can you calculate the distance?
That should help at the steps.
 
  • #4


got the centripetal force from f= mv2[itex]/[/itex]r

forgot to mention its a swing style ride

I am assuming a perfect release angle of 45 degrees... just to try and simplify...
 

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  • #5


mfb, you were assuming initial and final height were to be the same, which they are not. so you do need the initial height as well
[edit: also, i am a bit surprised you would calculate the time to go up and the time to go back down separately... but i guess it is a good excercise for the reader to see if they notice the symmetry :p then you completely do not need to calculate the height of the peak as well]

shini, centripetal force is irrelevant - it does not act after you have released the projectile.

angle of release may also not be 45 degrees. seems it actually is 0 degrees, i.e. moving entirely horizontally at release. it is not optimal for maximum distance, but i don't imagine you being able to impart any reasonable vertical component to the projectile velocity, so that is that. this actually simplifies the calculations a good bit.
 
  • #6


Looking at this ride, I see that an experimentalist could make the front page of both reddit and youtube by determining the result in the manner [STRIKE]prefered by[/STRIKE] unique to their profession.
 
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  • #7


georgir said:
mfb, you were assuming initial and final height were to be the same, which they are not. so you do need the initial height as well
No I were not.
[edit: also, i am a bit surprised you would calculate the time to go up and the time to go back down separately... but i guess it is a good excercise for the reader to see if they notice the symmetry :p then you completely do not need to calculate the height of the peak as well]
Do the calculation yourself, and you will see that this way avoids quadratic equations (it just requires to solve an equation of the type x^2=c for x).

angle of release may also not be 45 degrees. seems it actually is 0 degrees, i.e. moving entirely horizontally at release. it is not optimal for maximum distance, but i don't imagine you being able to impart any reasonable vertical component to the projectile velocity, so that is that. this actually simplifies the calculations a good bit.
I agree.
While 0° is not optimal*, it is quite close to that.


*looking at the context, I would think that "optimal" is more like "worst case" here.
 

1. How do I calculate the distance of a projectile at a theme park?

To calculate the distance of a projectile at a theme park, you will need to know the initial velocity of the projectile, the angle at which it is launched, and the gravitational acceleration. You can then use the formula: d = (v2sin2θ)/g, where d is the distance, v is the initial velocity, θ is the launch angle, and g is the gravitational acceleration (9.8 m/s2).

2. What is the importance of calculating projectile distance at a theme park?

Calculating projectile distance at a theme park is important for safety reasons. It allows theme park engineers to determine the safe distance for guests to stand from a ride or attraction, as well as the appropriate height and angle for launching projectiles to avoid any potential accidents.

3. How does air resistance affect the calculation of projectile distance?

Air resistance can affect the calculation of projectile distance by slowing down the projectile and reducing its range. To account for air resistance, you can use a more complex formula that takes into consideration the air density, cross-sectional area, and drag coefficient of the projectile.

4. Can I use the same formula to calculate projectile distance for all types of rides at a theme park?

No, the formula for calculating projectile distance may differ depending on the type of ride and the forces involved. For example, a roller coaster with a loop will have a different launch angle and initial velocity compared to a water ride with a steep drop. It is important to understand the specific factors and forces at play for each ride before calculating projectile distance.

5. How can I use the calculated projectile distance to improve ride design at a theme park?

The calculated projectile distance can be used to fine-tune and improve ride design at a theme park. By adjusting the initial velocity and launch angle, engineers can optimize the ride for maximum thrill and safety. It can also be used to determine the appropriate placement of safety barriers and other measures to keep guests safe.

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