Projectile Motion PDF

Characteristics of a Projectile's Trajectory ❖ A projectile is any object upon which the only force is gravity ❖ Projectiles travel with a parabolic trajectory due to the influence of gravity, ❖ There are no horizontal forces acting upon projectiles and thus no horizontal acceleration, ❖ The...

Characteristics of a Projectile's Trajectory ❖ A projectile is any object upon which the only force is gravity ❖ Projectiles travel with a parabolic trajectory due to the influence of gravity, ❖ There are no horizontal forces acting upon projectiles and thus no horizontal acceleration, ❖ The horizontal velocity of a projectile is constant (a never changing in value), ❖ There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down, ❖ The vertical velocity of a projectile changes by 9.8 m/s each second, ❖ The horizontal motion of a projectile is independent of its vertical motion. The important concept depicted in the above vector diagram is that the horizontal velocity remains constant during the course of the trajectory and the vertical velocity changes by 9.8 m/s every second. These same two concepts could be depicted by a table illustrating how the x- and y-component of the velocity vary with time.  HORIZONTAL “VELOCITY “COMPONENT ▪ It NEVER changes, covers equal displacements in equal time periods ▪ This means the initials horizontal velocity equals the final horizontal velocity. (CONSTANT) BUT WHY? Gravity DOES not work horizontally to increase or decrease the velocity.  VERTICAL “VELOCITY “COMPONENT ▪ Changes (due to gravity) does NOT cover equal displacements in equal time periods. Both magnitude and direction change. As the projectile moves up the MAGNITUDE DECREASES and its direction is UPWARD. As it moves down the MAGNITUDE INCREASES and the direction is DOWNWARD.  Component Magnitude Direction Horizontal Constant Constant Vertical Changes Changes These components produce what is called TRAJECTORY or path This path is called PARABOLIC in nature  HORIZONTALLY LAUNCHED PROJECTILES Projectiles which have NO upward trajectory and NO initial VERTICAL velocity  HORIZONTALLY LAUNCHED PROJECTILES To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction. 𝟏 𝟐 𝒙 = 𝒗𝒐𝒙 𝒕 𝒚= 𝒈𝒕 𝟐 Remember, the velocity is Remember that since the CONSTANT horizontally, so projectile is launched horizontally, that means the acceleration is the INITIAL VERTICAL VELOCITY is ZERO! equal to ZERO A plane travelling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will GIVEN UNKNOWN it land 𝑣 𝑜𝑥 =100 m/s t=? 1 y= 500 𝑚 X=? 𝑦 = 2 𝑔𝑡 2 500 m = 2 1 −9.8𝑚/𝑠 2 𝑡 2 𝑣𝑜𝑦 =0 m/s 2 102.04 s2 = 𝑡2 g= −9.80 𝑚/𝑠 𝑡 = 𝟏𝟎. 𝟏 𝒔 𝟏𝟎𝟎𝒎 𝒙 = 𝒗𝒐𝒙 𝒕 = 𝟏𝟎. 𝟏𝒔 = 𝟏𝟎𝟏𝟎 𝒎 𝒔