Calculating the trajectory of a projectile

In summary, the conversation is about a physics project where the speaker must build a water balloon launcher and calculate certain aspects of the trajectory, including initial velocity, maximum height, and angle of launch. They discuss using equations such as v = vo+at, x = xo+vot+(1/2)at2, and Range = v02sin2θ/g to find these unknowns. They also show their calculations for finding the initial velocity (v0y=22.40 m/s) and maximum height (25.57m). They ask for confirmation that their calculations are correct.
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Homework Statement


So, we have a physics project, in which we must build a water balloon launcher and launch the balloon at a stationary target about 50 yds away (normally we use meter, however we are firing on a football field). I have created my launcher (it is basically a slingshot), but now I must find certain aspects of the trajectory. I must find:
(a) Initial Velocity
(b) Maximum height
(c) Angle of Launch


Homework Equations


v = vo+at
x = xo+vot+(1/2)at2
v2 = vo2+2a(x-xo)
Range = v02sin2θ/g


The Attempt at a Solution


So, I know that my distance is 50 yds. I know my angle is 45o, because 45o is the degree at which one gets the most effective range. Now, for my time, I have not yet actually calculated it, so let's just say it's... 1.78 s (does that sound reasonable?). I am pretty sure that given this information, it shouldn't be too difficult for me to find my unknowns.
I'll attempt to start by finding the initial velocity... Now, initial velocity, I know, is quite a bit different from my average velocity (total distance/total time). So... I know that in the vertical direction, the velocity is affected by gravity, and (disregarding air resistance and such), there is no positive or negative velocity in the horizontal direction. I do have my angle. So, there is VoSin/Cos(theta)= Voy/ox. Umm... now I am a bit stuck...
Once I find the initial velocity, finding the maximum shouldn't be too hard, however I still may need a bit of help with it...

Or, perhaps Range = v0y2sin2θ/g
Range = 50 yd
v0y = ?
θ = 45
Ah, so that may work...
So, v0y=Square root((Range*g)/(Sin2θ))
So, v0y=Square root(( 45.72m*9.81m/s^2)/(Sin2(45))
So, v0y=22.40 m/s = 24.49 yd/s
Okay, so that's the initial velocity in the y direction. Progress.

So, VoSin(theta)= Voy Then:
Vo=?
theta=45
Voy=22.40 m/s
So then, Vo=26.32m/s. Awesome, found it. Still would like to make sure it's correct, so I will continue to post this.

So, now maximum height. I think I will go with v2= vo2+2a(s-so), using the y component.
v=0 (since the velocity in the y direction at max height is 0 )
v0y=22.40 m/s
a=-g
s=?
s0=0
SO, set up to solve for x... So, (-Vo^2)/(-2g). So, x=25.57m
Is that correct? If so, awesome. Thanks for all the help! haha.
 
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  • #2
*bump* so could someone just confirm that I did this correctly? Please? This is due tomorrow...
 

1. How do you calculate the trajectory of a projectile?

The trajectory of a projectile can be calculated using the following formula: y = y0 + x*tanθ - (g*x2)/(2*v02*cos2θ), where y is the height, y0 is the initial height, x is the horizontal distance, θ is the launch angle, g is the acceleration due to gravity, and v0 is the initial velocity.

2. What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by several factors, such as the initial velocity, launch angle, air resistance, and the force of gravity. Other factors that can affect trajectory include wind speed and direction, as well as the shape and weight of the projectile.

3. How does air resistance impact the trajectory of a projectile?

Air resistance can have a significant impact on the trajectory of a projectile. As the projectile moves through the air, it experiences a force in the opposite direction of its motion, which can cause it to slow down and deviate from its intended path. This is why objects with larger surface areas, such as feathers or parachutes, experience more air resistance and have a slower and more gradual descent compared to smaller, aerodynamic objects.

4. Can the trajectory of a projectile be predicted accurately?

The trajectory of a projectile can be predicted with a high degree of accuracy using mathematical equations and computer simulations. However, factors such as air resistance, wind, and slight variations in launch angle and initial velocity can affect the trajectory in real-world scenarios.

5. What are some real-world applications of calculating projectile trajectory?

Calculating the trajectory of a projectile has many practical applications, such as in the design of sports equipment (e.g. golf clubs, baseball bats), determining the optimal angle and speed for a projectile to hit a target, predicting the path of a rocket or satellite, and understanding the motion of objects in space. It is also crucial in fields such as ballistics and military operations.

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