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

In summary, the problem involves a particle with initial coordinates (sx, 0, sy, 0) being projected with a velocity of magnitude u at an angle of θ from a plane inclined at an angle of α. The particle undergoes no horizontal acceleration and its only vertical acceleration is -g ms-2. The equations for sx and sy in terms of time t are given, but the presence of the inclined plane makes the solution more difficult. It would be helpful to have the initial velocity and position given in terms of vx, vy, and vz.
  • #1
Big-Daddy
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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.

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

[tex]{s_x} = u \cdot \cos{θ} \cdot t[/tex]

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!
 
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  • #2
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).
 

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

What is an inclined plane projectile?

An inclined plane projectile is an object that is launched off of an inclined plane at an angle and follows a curved path due to the influence of gravity.

What factors affect the trajectory of an inclined plane projectile?

The angle of the inclined plane, the initial velocity of the projectile, and the force of gravity are all factors that affect the trajectory of an inclined plane projectile.

What is the purpose of studying inclined plane projectiles?

Studying inclined plane projectiles can help us understand the principles of motion and gravity, and can also have practical applications in fields such as engineering and ballistics.

How is the trajectory of an inclined plane projectile calculated?

The trajectory of an inclined plane projectile can be calculated using the equations of motion, taking into account the initial velocity, angle of the inclined plane, and acceleration due to gravity.

What are some real-life examples of inclined plane projectiles?

Examples of inclined plane projectiles include a ball rolling down a ramp, a rollercoaster car, and a ski jumper launching off of a hill.

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