In our study of circular motion Projectile motion

In our study of * circular motion ﺮﻛﺔ ﺍﻟﺪﺍﺋﺮﻳﺔ * Projectile motion ﺣﺮﻛﺔ ﺍﻟﻤﻘﺬﻭﻓﺎﺕ *tow and three dimensional motion ﺍﻟﺤﺮﻛﺔ ﻓﻲ ﺑﻌﺪﻳﻦ ﻭﻓﻲ ﺛﻼﺛﺔ ﺍﺑﻌﺎﺩ Average acceleration and Instantaneous Average velocity and acceleration instantaneous velocity Position and Displacement

Projectile Motion The projectile is launched with an initial velocity The horizontal and vertical velocity components are: g Projectile motion will be analyzed in a horizontal and a vertical motion along the x- and y-axes, respectively. These two motions are independent of each other. Motion along the x-axis has zero acceleration(so vx=constant). Motion along the y-axis has uniform acceleration ay = -g.

Projectile Motion Analyzed We consider a special case of two (x y plan ) dimensional motion. he particle moves in a vertical plane with initial velocity and its acceleration is always the free fall acceleration which is downward , this particle called projectile motion

To study of projectile motion we analyzed for two dimensional motion to the components for r , v, a y x 0 R

1 E q u 1: shows the path , velocity and acceleration for the projectile

4 - In projectile motion , the horizontal motion and the vertical motion are independent of each other. Projectile motion The horizontal motion The vertical motion

Projectile motion analyzed The horizontal motion Because there is no acceleration The vertical motion Because the acceleration is constant

The Equation of the path We can find the equation of the projectile’s path (its trajectory) by eliminating time t Because g , . , are constants Because a , b are constants. equation of parabola , The path is parabolic.

The Horizontal Range The horizontal range R of the projectile is the horizontal distance the projectile has traveled when it returns to its initial (launch ) height.

Range High Total time Angle

No because at certain instant vy ﻻﻥ ﻓﻲ ﻟﺤﻈﻯﺔ ﻣﻌﻴﻨﺔ ﻻ 0

Horizontal velocity (v) →vx constant. • Vertical velocity (v)→vy initially positive →decreases to zero, then • becomes negative. Horizontal acceleration (a)→ax= 0. • Vertical acceleration (a) →ay = - g. •

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