Initial Velocity - Projectile Motion

In summary, the individual is trying to calculate the vertical and horizontal displacement of a firework explosion using the given data of a time of 5.0 seconds and a height of 600 ft (182.88m). They have attempted to use equations v(i) = (d / t) - [(a * t) / 2] and V(i) = a*t, but are having difficulty deriving the initial velocity. They also wonder if it is possible to calculate the maximum height and final velocity of the shell at the time of break. The conversation concludes with the individual asking for help in incorporating air resistance into their calculations.
  • #1
vaio23
3
0
Hello,

My end goal is to calculate the vertical and horizontal displacement of an object that explodes in the air e.g. a firework. However, I am having difficulty deriving the initial velocity of the object. I know the approximate time is 5.0 seconds from the ground to explosion and the height is 600 ft (182.88m).

So far I have used the equations v(i) = (d / t) - [(a * t) / 2] and V(i) = a*t. Any help would be greatly appreciated.
 
Physics news on Phys.org
  • #2
The initial velocity to fire is the same as the velocity an object would be traveling at after falling from its peak altitude.

Formulas and calculator can be found here:
http://www.gravitycalc.com/

If the time is 5 seconds, the altitude would be 123 meters and the initial velocity would be 49 meters/second.

If the altitude is 183 meters, the time is 6.1 seconds at an initial velocity of 59 meters/second.
 
  • #3
The 600 ft (182.88m) is the height in which the fireworks breaks and we do know from industry averages that a shell of this size takes 5.0 seconds to reach this height. It is likely that the maximum height is greater than 600 ft which would mean the shell still has a final velocity at the time of break. Is there a way to calculate for these two unknowns?
 
  • #4
vaio23 said:
So far I have used the equations v(i) = (d / t) - [(a * t) / 2] and V(i) = a*t. Any help would be greatly appreciated.
The first equation is fine. That will tell you the initial velocity (vertical component only) which will allow the projectile to reach a given height in a given time. Note that this neglects air resistance, which may well be significant.

There's no way to determine the horizontal component of velocity from the given data.
 
  • #5
Thank you for your response it was a big help. If I wanted to become more precise and incorporate air resistance into my formula how would I do this. It was been a long time since I've done something like this.

Known Values:
Time = 3.8
Aprox Height = 300 Ft
Initial velocity = 140 Ft/s
Launch Angle = 75 Degrees
Weight of shell = 3.5 lbs
Also, the radius of the sphere is 3 inches
 

1. What is initial velocity in projectile motion?

Initial velocity is the velocity at which an object starts moving in projectile motion. It is a vector quantity, meaning it has both magnitude (speed) and direction. In projectile motion, the direction of the initial velocity is typically horizontal.

2. How is initial velocity calculated?

Initial velocity can be calculated using the formula V₀ = v * cos(θ), where V₀ is the initial velocity, v is the initial speed, and θ is the initial angle of launch. This formula assumes that the initial velocity is at a horizontal angle.

3. Can initial velocity be negative?

Yes, initial velocity can be negative if the object is launched in the opposite direction of its initial motion. In projectile motion, a negative initial velocity would indicate that the object is launched downwards, while a positive initial velocity would indicate an upwards launch.

4. How does initial velocity affect the trajectory of a projectile?

The magnitude and direction of the initial velocity directly affect the trajectory of a projectile. A higher initial velocity will result in a longer horizontal range, while a lower initial velocity will result in a shorter range. The direction of the initial velocity also plays a role, as a higher angle of launch will result in a higher and shorter trajectory, while a lower angle of launch will result in a lower and longer trajectory.

5. What factors can affect the initial velocity of a projectile?

The initial velocity of a projectile can be affected by factors such as the angle of launch, the initial speed, and external forces such as air resistance. Other factors such as the shape and mass of the object can also play a role in determining the initial velocity.

Similar threads

Replies
3
Views
799
Replies
4
Views
994
Replies
8
Views
2K
Replies
8
Views
2K
Replies
17
Views
17K
Replies
5
Views
1K
  • Mechanics
Replies
18
Views
2K
Replies
13
Views
3K
Replies
9
Views
2K
Replies
12
Views
3K
Back
Top