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In this chapter, we’ll use vectors to expand our understanding of forces and motion into two dimensions. Most real-world physics problems (such as with the game of pool pictured here) are, after all, either two- or three-dimensional problems and physics is most useful when applied to real physical scenarios. We start by learning the practical skills of graphically adding and subtracting vectors (by using drawings) and analytically (with math). Once we’re able to work with two-dimensional vectors, we apply these skills to problems of projectile motion, inclined planes, and harmonic motion.

You want a projectile to fly as far as possible, at which angle should you launch it? We'll start with formulas for the initial velocity.

This video explains how pie charts can be used to display data in a more 'user-friendly' way.

This video explains how to plot straight line graphs.

Plotting projectile displacement, acceleration, and velocity as a function of time.

Video 1: Introduces the concept of prime factorisation
Video 2: Examples of prime factorisation
Video 3: Common mistakes made relating to prime factorisation

This video looks at set notation, Venn diagrams and probability.

Online problems where the student is required to simplify the expression using the product property of exponents.

Figuring out the horizontal displacement for a projectile launched at an angle.

• Determine how each parameter (initial height, initial angle, initial speed, mass, diameter, and altitude) affects the trajectory of an object, with and without air resistance.
• Predict how varying the initial conditions will affect a projectile’s path, and provide an explanation for the prediction.
• Estimate where an object will land, given its initial conditions.
• Determine that the x and y motion of a projectile are independent.
• Investigate the variables that affect the drag force.
• Describe the the effect that the drag force has on the velocity and acceleration.
• Discuss projectile motion using common vocabulary (such as: launch angle, initial speed, initial height, range, time).