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Projectile MotionThis follows on from M1 Kinematics. Note this is in M1 for the AQA syllabus MM1A and MM1B! Equations of motionConsider a particle projected at a speed u at an angle Thus we can resolve the velocity in two components and apply the equation The horizontal component of the velocity is The vertical component of the velocity is Finding the rangeThe range is the total distance travelled horizontally. This can be found by calculating the values of x for which So putting
So either Obviously t = 0 is at the start of the motion. So input the value of t into the equation for x to obtain
Using the double angle formula
And this is the range.
Finding the time of flightThe time of flight can be found by calculating the value of t when x = range. So using we get The time of flight =
The equation of motion of a projectileThe equations Expressing Substituting in
Which tidies up to give Then Using the identity the equation of motion of a projectile is |
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