Chapter 3: Vectors and motion Notes

Sections

1. 3A Displacement and velocity vectors Mastered

   Position and displacement vectors, motion with constant velocity, speed as the magnitude of velocity, finding when and where a moving object reaches a line, and closest approach using the dot product.

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2. 3B Calculus with vectors Mastered

   Differentiating position vectors to find velocity and acceleration vectors, speed, integrating acceleration and velocity vectors using initial conditions, and analysing motion in the plane.

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3. 3C Resultants of forces and velocities Mastered

   Adding forces and velocities as vectors, the resultant of two forces using components or the cosine rule, forces in equilibrium, and boats and planes moving through currents and winds.

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4. 3D Projectile motion Mastered

   Specifying velocity by speed and angle or by components, deriving the equations of motion of a projectile from the acceleration vector, time of flight, greatest height, range, and the velocity at any time.

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5. 3E The path of a projectile Mastered

   Eliminating t to find the Cartesian equation of a projectile's path, the general range formula and the angle of maximum range, finding the launch angle needed to hit a target, and projectiles launched from a height.

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