Projectile motion calculations from data gathered during trials

In summary: Therefore, in summary, the solution for the projectile motion formulas for \Theta and v_0 are \Theta=\pi and v_0=-6.75 m/s, respectively.
  • #1
wortman
4
0

Homework Statement


solve projectile motion formulas for [tex]\Theta[/tex] and [tex]v_0[/tex]
all measurements are in m, t is seconds
[tex]y_0=.005[/tex]
[tex]x_0=0[/tex]
the averages from my trials were:
[tex]x=8.775 m[/tex]
[tex]t=1.3 s[/tex]

Homework Equations


[tex]x=x_0+v_0*cos\Theta*t[/tex]
[tex]y=y_0+v_0*sin\Theta*t+.5a_yt^2[/tex]

The Attempt at a Solution


after plugging in my numbers gives:
for x
[tex]6.75=v_0*cos\Theta[/tex]
which as far as I can see still has two unknowns, where do I go from here?

I'm pretty confused about the y component because I'm not even sure what y is supposed to be. Don't I need a y(max) number first?
 
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  • #2


Hello,

To solve for \Theta and v_0, you will need to use both equations and solve for the unknowns simultaneously. Let's start with the x equation:

x=x_0+v_0*cos\Theta*t
Substituting in the given values:
8.775=0+v_0*cos\Theta*1.3
Solving for v_0*cos\Theta:
v_0*cos\Theta=8.775/1.3=6.75
Now, let's move on to the y equation:
y=y_0+v_0*sin\Theta*t+.5a_yt^2
Substituting in the given values:
0.005=v_0*sin\Theta*1.3+.5*(-9.8)*1.3^2
Simplifying:
0.005=v_0*sin\Theta*1.3-8.047
Solving for v_0*sin\Theta:
v_0*sin\Theta=(0.005+8.047)/1.3=6.75
Now, we have two equations with two unknowns (v_0*cos\Theta and v_0*sin\Theta). We can solve for these unknowns by using the Pythagorean theorem:
(v_0*cos\Theta)^2+(v_0*sin\Theta)^2=(6.75)^2
Substituting in the values we found earlier:
(6.75)^2=(6.75)^2+(v_0*sin\Theta)^2
Solving for v_0*sin\Theta:
(v_0*sin\Theta)^2=0
v_0*sin\Theta=0
Substituting back into the equation for v_0*cos\Theta:
v_0*cos\Theta=6.75
Now, we have two equations with two unknowns (v_0 and \Theta). We can solve for these unknowns by dividing the first equation by the second:
(v_0*cos\Theta)/(v_0*sin\Theta)=6.75/0
cos\Theta/sin\Theta=6.75/0
tan\Theta=0
Solving for \Theta:
\Theta=0 or \pi
Since \Theta cannot be 0 (this would result in a straight line trajectory), the only valid solution is \Theta=\pi. Now, we can substitute this value back into either of the original
 
  • #3


I would suggest starting by reviewing the equations for projectile motion and making sure all the variables are clearly defined. In this case, it seems like you have the initial position (x0 and y0), but it's not clear what the initial velocity (v0) or the acceleration (ay) are. Without these values, it will be difficult to solve for the unknowns.

Once all the variables are defined, you can use the given data (x=8.775 m and t=1.3 s) to solve for the initial velocity (v0) using the equation x=x0+v0*cosθ*t. From there, you can use the value of v0 to solve for the angle (θ) using the equation 6.75=v0*cosθ. Finally, you can use the value of v0 to solve for the acceleration (ay) using the equation y=y0+v0*sinθ*t+0.5*ay*t^2.

It's also important to note that the y component of the projectile motion will depend on the initial velocity and angle, as well as the acceleration due to gravity (g). Without knowing the initial velocity and angle, it will be difficult to determine the maximum height (ymax) or any other y component of the motion. It may be helpful to review the concept of projectile motion and make sure you have all the necessary information before attempting to solve for the unknowns.
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path known as a parabola.

2. How do you calculate projectile motion from data gathered during trials?

To calculate projectile motion, you will need to gather data about the initial velocity, angle of launch, and the time the object spent in the air during each trial. You can then use these values to calculate the horizontal and vertical components of the object's velocity and acceleration, and plot its motion on a graph.

3. What is the formula for calculating projectile motion?

The formula for calculating projectile motion is: x = v0cos(θ)t for the horizontal distance and y = v0sin(θ)t - 0.5gt2 for the vertical distance, where x and y are the horizontal and vertical distances, v0 is the initial velocity, θ is the angle of launch, t is the time, and g is the acceleration due to gravity.

4. What factors can affect projectile motion?

The factors that can affect projectile motion include the initial velocity, angle of launch, air resistance, and the acceleration due to gravity. Other factors such as wind, temperature, and the shape of the object can also have an impact on the motion.

5. How can projectile motion calculations be applied in real life?

Projectile motion calculations can be applied in various fields such as sports, engineering, and physics. For example, in sports, understanding projectile motion can help athletes determine the optimal angle and velocity for throwing or kicking a ball. In engineering, it can be used to design and test the trajectory of objects such as rockets or projectiles. In physics, it is used to study the motion of objects in freefall or in a vacuum.

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