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The following plot shows the trajectory of a projectile launched with an initial velocity of 10 m/s, at an angle of 45 and with no initial height (dashed line).
- the path of a moving object is called its trajectory (Latin trajectus means ‘crossing’ or ‘passage’ - a projectile is an object that once given an initial thrust, it moves through the air only under the force of gravity
projectiles launched horizontally have no initial vertical velocity. as a result, the vertical motion is identical to that of a dropped object. the downward velocity increases due to the acceleration due to gravity.
Projectile Motion Definition: • body of mass m launched with speed v0 at angle θ from the horizontal; • air resistance F P res = − b v P , b = nonnegative constant (possibly zero) x z F = –mg m θ z v 0 Prerequisites: • fundamentals of Newtonian mechanics • motion in one dimension, with and without res-istance Why study it?
5 PROJECTILES. Objectives. After studying this chapter you should. • recognise that projectile motion is common; • understand how to obtain a simple mathematical model of projectile motion; • be able to validate the model; mple problems of projectile motion;• know how to use the model to invest.
Cartesian Equation of Motion: = −𝑔𝑥 2𝑉2 (1+tan2𝜃)+ tan𝜃 Time of Flight: 𝑡=2𝑉sin𝜃 𝑔 Maximum Range: =𝑉 2 𝑔 Maximum Height: =𝑉 2sin2𝜃 2𝑔
Projectile motion can be treated as two rectilinear motions, one in the horizontal direction experiencing zero acceleration and the other in the vertical direction experiencing constant acceleration (i.e., gravity). For illustration, consider the two balls on the left.
