Note: All Khan Academy content is available for free at (www.khanacademy.org)

Note: All Khan Academy content is available for free at (www.khanacademy.org)

Conservation of energy is used to solve a projectile motion problem and to analyse the motion of a pendulum bob. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Calculus is used to solve the same problem as in the previous video. Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

How to calculate the direction that a speedboat of fixed speed must travel in in order to get as close as possible to a yacht moving with constant velocity. A geometrical approach is used here. In the next video, calculus is used. Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Relative Velocity. The angle that a boat must enter a river in order to go directly across the river. Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

All the velocity vectors are constant. V_ab = V_a - V_b Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

18:16 (2013) How to calculate the launch angle Ɵ of a particle to an incline of given angle β in order to get the maximum range for the particle fired up the incline with given speed u. We see that Ɵ does not depend on u. Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

For any given launch speed u, the angle that gives the maximum range of the particle is 45 degrees. Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Sample problems involving vectors. Check out KeysToMaths1 for more tutorials: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

Sample problems with vectors.

Two numbers give the polar form of a vector in two dimensions, the length or magnitude r of the vector, and the angle theta measured anti - clockwise from the positive x-axis to the vector.

The i - j plane contains vectors which are built up from the unit vectors (length = 1) i and j. i points up and j points to the right.

Lesson on representing a vector in three dimensions.

Lesson 2 on vectors and their inherent properties.

Lesson and overview of vectors and their inherent properties.

How to denote unit vectors. Note: All Khan Academy content is available for free at (www.khanacademy.org)

Lesson on multiplying vectors by scalars. Note: All Khan Academy content is available for free at (www.khanacademy.org)

Lesson on adding vectors and vector components. Note: All Khan Academy content is available for free at (www.khanacademy.org)

Tutorial on vectors and vector spaces. Note: All Khan Academy content is available for free at (www.khanacademy.org)

Brendan Willimason explains the course content relevant to question 3 The worksheet for this lecture can be found at http://sites.duke.edu/brendanwilliamson/files/2013/10/Worksheet-2.pdf