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

Click For Summary
SUMMARY

The equations for projectile motion on an inclined plane involve determining the particle's position over time, factoring in the incline's angle and gravitational acceleration. The initial position is defined as (sx, 0, sy, 0), with the particle projected at an angle θ from the plane. The vertical motion equation is given by sy = u * sin(θ) * t - (1/2) * g * t^2, and the horizontal motion equation is sx = u * cos(θ) * t, where g is the gravitational acceleration of 9.8 m/s². Understanding these equations is essential for solving projectile motion problems on inclined planes.

PREREQUISITES
  • Understanding of basic kinematics and projectile motion
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of gravitational acceleration (g = 9.8 m/s²)
  • Ability to manipulate equations involving time and motion
NEXT STEPS
  • Study the derivation of projectile motion equations on inclined planes
  • Learn about vector decomposition in physics
  • Explore advanced kinematics involving multiple dimensions
  • Investigate the effects of varying angles of inclination on projectile trajectories
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators teaching projectile motion concepts in inclined planes.

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.

[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!
 
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).
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
2K
Replies
7
Views
2K
  • · Replies 18 ·
Replies
18
Views
6K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
Replies
3
Views
2K