Projectile Motion and acceleration of particle

[AkshayM]

Homework Statement

If a particle moves in X-Y plane with acceleration non zero in X and Y , the particle will not move in a parabolic path
True or False ?

Homework Equations

X = UxT + 1/2(Ax)T^2
Y= UyT + 1/2 (Ay)T^2

The Attempt at a Solution

The equation of trajectory that i came up with involved Y^2 , X^1/2 and X
I am not able to draw conclusions with it
So i guessed it to be True as for a parabolic path you need constant acc in only one axis and zero acc in other axis
But the book says false
Please help !

 

[berkeman]

Welcome to the PF.

Think about how a projectile traces out a parabolic shape when you throw it up and out at a 45 degree angle. What forces and accelerations are acting on it in that situation (after it leaves your hand)?

 

[AkshayM]

Welcome to the PF.

Think about how a projectile traces out a parabolic shape when you throw it up and out at a 45 degree angle. What forces and accelerations are acting on it in that situation (after it leaves your hand)?

Welcome to the PF.

Think about how a projectile traces out a parabolic shape when you throw it up and out at a 45 degree angle. What forces and accelerations are acting on it in that situation (after it leaves your hand)?

Just the gravity pull and air friction

 

[berkeman]

Just the gravity pull and air friction

Good. So neglecting air friction (which will alter the path away from a pure parabola), in how many dimensions is the projectile accelerating while it traces out the parabola?

 

[AkshayM]

Good. So neglecting air friction (which will alter the path away from a pure parabola), in how many dimensions is the projectile accelerating while it traces out the parabola?

2 dimensional motion with downward acceleration (g)

 

[berkeman]

@AkshayM -- You marked this thread as solved -- does that mean you understand now?

 

[AkshayM]

@AkshayM -- You marked this thread as solved -- does that mean you understand now?

Sorry no bymistakely i did it

 

[berkeman]

If a particle moves in X-Y plane with acceleration non zero in X and Y , the particle will not move in a parabolic path
True or False ?

But the book says false

So the book is saying that the path is parabolic even when there is acceleration in 2 dimensions?

 

[AkshayM]

So the book is saying that the path is parabolic even when there is acceleration in 2 dimensions?

Yes it says parabolic path
Case of a misprint ?

 

[berkeman]

Maybe. Can you ask the professor or a TA about it? Do you know any other students in your class who are also working on the problem?

 

[haruspex]

Homework Statement

If a particle moves in X-Y plane with acceleration non zero in X and Y , the particle will not move in a parabolic path
True or False ?

Homework Equations

X = UxT + 1/2(Ax)T^2
Y= UyT + 1/2 (Ay)T^2

The Attempt at a Solution

The equation of trajectory that i came up with involved Y^2 , X^1/2 and X
I am not able to draw conclusions with it
So i guessed it to be True as for a parabolic path you need constant acc in only one axis and zero acc in other axis
But the book says false
Please help !

First, let us be clear that the question is asking whether a nonzero acceleration in both coordinates guarantees that it will not be a parabola. My point is nothing has been said about constancy of acceleration, so certainly it might not be a parabola.

So now suppose there is constant acceleration in each coordinate. What if you were to use different axes? Might there be a direction in which there is no acceleration? Will there always be such a direction?

 

[Ray Vickson]

Yes it says parabolic path
Case of a misprint ?

To re-express the answer of haruspex in post #11: if you take the path to be $x = v_x t + \frac{1}{2} a_x t^2$ and $y = v_y t + \frac{1}{2} a_y t^2,$ (with constants $v_x, v_y, a_x,a_y$) can you find a constant angle $\theta$ and a rotated coordinate system
$$\begin{array}{rcl}
X&=& x \cos(\theta) - y \sin (\theta)\\
Y&=& x \sin (\theta) + y \cos (\theta)
\end{array} $$ in which the new path has the form $X = U_x t, \; Y = U_y t + \frac{1}{2} W_y t^2,$ (with constant $U_x, U_y, W_y$) or is that not possible? If it is possible, that would give you a "rotated" parabola.