2 Mechanics - Pearson Global Schools

Horizontal componentsAt A (time 0)Displacement zeroVelocity v cos Acceleration 0At B (time __ t ) At C (time t)2Displacement R __2Velocity v cos Acceleration 0Displacement RVelocity v cos Acceleration 0Vertical componentsAt A At B At CDisplacement zeroVelocity v sin Acceleration gDisplacement hVelocity zeroAcceleration gDisplacement zeroVelocity v sin Acceleration gWe can see that the vertical motion is constant acceleration and the horizontalmotion is constant velocity. We can therefore use the suvat equations.suvat for horizontal motionSince acceleration is zero there is only one equation needed to define the motionsuvatVelocity v s _tA to CR v cos tParabolic pathSince the horizontal displacementis proportional to t the path has thesame shape as a graph of verticaldisplacement plotted against time.This is parabolic since the verticaldisplacement is proportional to t 2 .suvat for vertical motionWhen considering the vertical motion it is worth splitting the motion into two parts.suvat At B At Cs 1_ (u v)t2v 2 u 2 2ass ut 1_2 at2a ______ v uth 1_2 (v sin ) t __20 v 2 sin 2 2ghh v sin t 1_2 g ( t __2) 2g v sin 0 _________t__20 1_ (v sin v sin )t2(v sin ) 2 (v sin ) 2 00 v sin t 1_2 gt2g _______________v sin v sin tSome of these equations are not very useful since they simply state that 0 0.However we do end up with three useful ones (highlighted) :R v cos t (1)0 v 2 sin 2 2gh or h _______ v2 sin 2 (2)2g0 v sin t 1_ 2 gt2 or t ______ 2v sin g (3)Solving problemsIn a typical problem you will be given the magnitude and direction of the initialvelocity and asked to find either the maximum height or range. To calculate hyou can use equation (2) but to calculate R you need to find the time of flight somust use (3) first (you could also substitute for t into equation (1) to give a fourthequation but maybe we have enough equations already).You do not have to remember a lot of equations to solve a projectile problem. Ifyou understand how to apply the suvat equations to the two components of theprojectile motion, you only have to remember the suvat equations (and they are inthe databook).Maximum rangeFor a given value of v the maximumrange is when v cos t is amaximum value. Now t ______ 2v sin g .If we substitute this for t we getR ___________2v2 cos sin g .This is a maximum when cos sinis maximum, which is when 45°.29