What are the equations for projectile motion on an inclined plane?

AI Thread Summary
The discussion focuses on deriving equations for projectile motion on an inclined plane. A particle is projected with an initial velocity at an angle from the plane, and the challenge lies in accounting for the incline while calculating the horizontal and vertical displacements over time. The basic equations for motion without incline are provided, but participants express confusion about adapting these to the inclined scenario. There is a suggestion that clearer initial conditions and a more detailed breakdown of the velocity components would aid in solving the problem. The conversation highlights the complexity introduced by the incline, emphasizing the need for a structured approach to find the correct expressions for displacement.
Big-Daddy
Messages
333
Reaction score
1

Homework Statement


A particle of mass m is projected with velocity of magnitude u at an angle of θ, measured anticlockwise from the line parallel to the plane, from a point (sx,0,sy,0) on a plane inclined at an angle of α measured anticlockwise from the line parallel to the ground. The particle coordinates refer to the particle's initial position (it starts from the plane) relative to the ground (i.e. sx is on an x-axis parallel to the ground, sy is on a y-axis perpendicular to the ground).
Find an expression each for sx and sy in times of time t, given that the particle undergoes no horizontal acceleration and that its only vertical acceleration is -g ms-2.

Homework Equations


I don't know. We have to find the equation.

The Attempt at a Solution



Well if the plane were not inclined this would be pretty easy.

{s_y} = u \cdot \sin{θ} \cdot t + \frac{1}{2} \cdot {a_y} \cdot t^2

{s_x} = u \cdot \cos{θ} \cdot t

Where θ is the angle of projection, and ay happens to be -g=-9.8 ms-2 in this case.

But now that the plane is inclined, I really am not sure!
 
Physics news on Phys.org
Gives me a headache just to figure the problem.

Would be good if the initial velocity were given in terms of v = vx i + vy j + vz k as well as its initial position (x0, y0, z0). Or if it's 2-dimensional (I can't tell from the wording), leave out the z0 and vz k. Then we could compute x(t), y(t) and (if appropriate) z(t).
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top