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The document provides three examples of projectile motion calculations. The first example calculates the height and vertical velocity of a ball thrown at 10 m/s for 5 seconds. The second example finds the maximum height, horizontal displacement, and time for a ball kicked at 10 m/s and an angle of 53 degrees.
The trajectory of a projectile can be found by eliminating the time variable t from the kinematic equations for arbitrary t and solving for y(x). We take x 0 = y 0 = 0 x 0 = y 0 = 0 so the projectile is launched from the origin.
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?
- 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
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).
Common examples include: elasticity (force is proportional to displacement); resistance to motion through a fluid (force is a function of velocity).
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.
