Projectile motion calculations


As we have seen in previous lessons, projectiles can be broken into vertical and horizontal components.

  • The horizontal component of initial velocity
    • Ux = u cos θ
  • The vertical component of initial velocity
    • Uy = u sin θ

Projectile motion can be modelled using the following equations:

To use these as x and y components, remember that the acceleration in the x plane is 0 and the acceleration in the y plane is g (9.8 m/s/s)

We derive the following equations for the y direction

  • vy = uy + gt
  • sy = uyt + ½ g t2
  • vy2 = uy2 + 2 g s

As well as the following for the x direction

  • vx = ux
  • sx = ux
  • vx2 = ux2


You only need to memorize.

You can derive the other equations from what is on your formula sheet.


The following will be HSC style projectile motion questions.

Question 1 a. [1 mark]

A potato launcher releases potato’s at an angle of 35° to the horizontal, it’s muzzle velocity is 400 m/s. What are the initial horizontal and vertical components of the velocity of the potato?

Question 1 b. [2 marks]

What are the vertical and horizontal components of the potato 5 seconds after it has been launched?

Question 1 c. [3 marks]

What is the range of the potato launcher?

Question 2. [3 marks]

A tennis ball is hit 1.5 m from the ground, it reaches a maximum height of 36.5 m with an initial angle of 60°, what was it’s initial speed?

Question 3 a. [3 marks]

A tennis ball is thrown from the top of the wall where with a launch height of 12 m above the ground. It has an initial velocity of 12 m/s at an angle of 40° from the horizontal. How long is the ball in the air for?

Question 3 b. [3 marks]

What would the final velocity of the tennis ball be before it hits the ground?

Question 4. [3 mark]

An archer is 50 m away from a target, he shoots his arrow at 60 km/ h. What angle must he aim at to hit the target?

Question 5. [3 marks] (extension)

A ball is thrown off a cliff 30 degrees down from the horizontal. If the ball lands 60 m from the cliff, where the height of the cliff is 42 m, with a final velocity of 15 m/s 110 degrees from the horizontal. What is the initial velocity of the ball?


Question 3.

a) 0.1 sec

b) 13 at 175 degrees

Question 4.

3.9 *10^-6 degrees up from horizontal

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