Results

By the end of this unit you will be able to:

• Understand when to use Venn diagrams.
• Draw Venn diagrams.
• Interpret Venn diagrams.

Outcomes:

• Design a diet and exercise regimen.
• Estimate the number of calories required for basic survival.
• Estimate the number of calories burned by exercise.
• Explain how heart health depends on diet and exercise.
• Explain how Body Mass Index (BMI) depends on weight and height.

• Identify when forces are balanced vs unbalanced.
• Determine the sum of forces (net force) on an object with more than one force on it.
• Predict the motion of an object with zero net force.
• Predict the direction of motion given a combination of forces.

Determining how fast something will be traveling upon impact when it is released from a given height. 

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.

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

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

• 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).

Visualising position, velocity and acceleration in two-dimensions for projectile motion.

Sometimes, when the probability problems are complex, it can be helpful to graph the situation. Tree diagrams and Venn diagrams are two tools that can be used to visualize and solve conditional probabilities.

This online lesson explores these two tools.