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Projectile Motion

Physics: AQA A Level, topic 4.1.12

Projectile Motion

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory. We assume air resistance is negligible.

Horizontal and vertical

Horizontal and vertical

  • The most important thing to remember about projectile motion is that the horizontal and vertical components of the problem are independent.
  • This means we can solve two sets of equations, one for each direction.
Components of displacement

Components of displacement

  • This diagram shows the displacement, s, of a football at a point along its path (trajectory).
  • The displacement vector has components sx (along the horizontal axis) and sy (along the vertical axis).
  • Its magnitude is s, and it makes an angle θ with the horizontal.
  • The vertical component is sy = s sinθ.
  • The horizontal component is sx = s cosθ.
Components of acceleration

Components of acceleration

  • Projectiles are only acted upon by one force: gravity.
  • Therefore, the vertical component of acceleration, ay, is equal to the acceleration due to gravity.
  • ay = g = −9.81m/s².
    • Remember the minus sign!
  • There is no force acting in the horizontal direction, so the horizontal component of acceleration, ax, is zero.
  • ax = 0.
Components of velocity

Components of velocity

  • Velocity can also be separated into components.
  • For a projectile travelling at an angle θ at a velocity v:
  • vy = v sinθ
  • vx = v cosθ

Projectile Motion - Worked Example

The following steps can be used to solve problems with projectile motion.

Step 1 - resolve components

Step 1 - resolve components

  • Find the horizontal information:
  • sx, ux, vx and ax (this will be zero).
  • Find the vertical information:
  • sy, uy, vy and ay (this will be g = -9.81m/s²).
  • Time, t, is the same in each component.
Step 2 - choose equations for each part

Step 2 - choose equations for each part

  • Choose which of the 'suvat' equations you need to use for each component of motion.
  • Remember the equation you need for the vertical part may be different to the one you need for the horizontal.
Step 3 - solve each component of motion

Step 3 - solve each component of motion

  • Use the 'suvat' equation you've identified to solve each component of motion.
  • Remember to solve them separately.
Step 4 - recombine the variables

Step 4 - recombine the variables

  • If you need to, you can find the total velocity vector, displacement vector and angle by recombining the components of the vector.
  • s=sx2+sy2s = \sqrt{s_x^2 + s_y^2}
  • v=vx2+vy2v = \sqrt{v_x^2 + v_y^2}
  • θ=tan⁡−1(vxvy)=tan⁡−1(sxsy)\theta = \tan^{-1}(\frac{v_x}{v_y}) = \tan^{-1}(\frac{s_x}{s_y})

Test yourself on Projectile Motion

  • What are the magnitudes of the horizontal and the vertical components of acceleration?

  • What is the equation for the final velocity?

  • Solving Projectile Motion Problems

Practise this topic for free