Conservation of energy is used to solve a projectile motion problem and to analyse the motion of a pendulum bob.
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All the velocity vectors are constant.
V_ab = V_a - V_b
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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
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.
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