# (Projectile Motion)How to derive the equation?

• herfox
In summary, the conversation is about deriving an equation to determine the distance traveled by a ping pong ball launched by an elastic band at a constant 36 degree angle. The data collected shows a curved relationship between the stretch and distance traveled. The group discusses different methods of determining the equation, such as using a power regression or the log-log approach. Finally, they come up with the equation s = a * x^2, with a being a constant determined by the other variables.
herfox
(Projectile Motion)How to derive the equation??

I made a device which use elastic band to launch a ping pong ball.
I have measured the distance traveled with different length of stretch at constant 36 degree launch angle. The graph plotted out is kind of curved, not straight line. And now I am asked to derive an equation to determine distance as a function of stretch...
Does anyone know how to do this? Cuz I spent almost a day still duno how to do it.

herfox said:
I made a device which use elastic band to launch a ping pong ball.
I have measured the distance traveled with different length of stretch at constant 36 degree launch angle. The graph plotted out is kind of curved, not straight line. And now I am asked to derive an equation to determine distance as a function of stretch...
Does anyone know how to do this? Cuz I spent almost a day still duno how to do it.
First, determine what kind of relationship it is (i.e. exponential, root...). WHat kind is it?

Well... i don't really know actually. I guess its root maybe?
heres the data
Stretch(cm) Distance(m)
10.7 5.684
15.35 7.955
20.12 9.98
24.96 10.365
29.83 11.725

Last edited:
herfox said:
Well... i don't really know actually. I guess its root maybe?
heres the data
Stretch(cm) Distance(m)
10.7 5.684
15.35 7.955
20.12 9.98
24.96 10.365
29.83 11.725
Wait a minute, let me enter the data in my calc

Well, it's hard to tell for sure. If you had more points, it would be easier to determine. The first 3 points look linear, but with the last 2 points, it looks more like a root relationship.

oh... yaa that's what the graph looks like...
alright maybe I got to do more points then.
Anywayz, Thanks a lot!

If you think the data is related by a power function you can try a power regression on your calculator. In the old days, the power was usually found by graphing the log of the distance and the log of the stretch to decipher the exponent from the slope of what would then be a linear graph. If your calculator can't do it, I can elaborate on the log-log approach

Last edited:
You may want to try.. y/x and y/x^2 ... y/sqrt(x) and so on, which gets you the constant of proportionality k ... and see which one is more consistent

of course it's a curve
here's the equation

v=u+at (vertical motion)
-u sin36=u sin36 -gt
t=2u sin36/g

s=ut
s= u sin36 * 2 u sin36/g
s= u*u *2 *sin36 *cos36 / g

but
mv*v/2= kx*x/2
mu*u/2=kx*x/2

u*u=kx*x/m

then

s=kx*x *2 *sin36 *cos36 / gm

as all the other variables remain constant

if a=k*2 *sin36 *cos36 / gm

s= a * x^2

## 1. What is projectile motion?

Projectile motion is the motion of an object that is thrown, launched, or otherwise projected into the air and then moves along a curved path under the influence of gravity.

## 2. What is the equation for projectile motion?

The equation for projectile motion is y = y0 + (v0sinθ)t - 1/2gt2, where y0 is the initial height, v0 is the initial velocity, θ is the launch angle, t is the time, and g is the acceleration due to gravity.

## 3. How is the equation for projectile motion derived?

The equation for projectile motion is derived using the principles of kinematics and the laws of motion. By analyzing the forces acting on the projectile and the relationships between displacement, velocity, and acceleration, the equation can be derived.

## 4. Can the equation for projectile motion be used for any object?

The equation for projectile motion can be used for any object that is launched or thrown into the air, as long as it is subject to the force of gravity and there is no significant air resistance. This includes objects such as balls, arrows, and even rockets.

## 5. Why is the equation for projectile motion important?

The equation for projectile motion is important because it allows scientists and engineers to predict the trajectory of a projectile and understand its motion. This is useful in a variety of fields, including sports, military operations, and space exploration.

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