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# Grade 10 phy: Projectile Motion

CHAPTER ONE: MOTION IN TWO DIMENSION

1.1 Projectile Motion

•   Projectile motion is the motion of an object that is projected into air at an angle.
• Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory.
• Projectile motion is a special case of two-dimensional motion.
• A particle moving in a vertical plane with an initial velocity and experiencing a free-fall (downward) acceleration, displays projectile motion.
• Some examples of projectile motion are:
• The motion of a cannon ball
• The motion of stone thrown horizontally
• The motion of volley ball, tennis ball.
• The motion of a billiard ball on the billiard table.
• A motion of a shell fired from a gun.

Assumptions of Projectile Motion

• The free-fall acceleration is constant over the range of motion
• It is directed downward.
• The effect of air friction is negligible.
• With these assumptions, an object in projectile motion will follow a parabolic path. This path is called the trajectory

Projectile Motion Diagram fig. projectile motion

• We analyze two-dimensional projectile motion by breaking it into two independent one dimensional motions along the vertical and horizontal axes.
• The horizontal motion is simple, because ax=0 and vx is thus constant.
• The velocity in the vertical direction begins to decrease as the object rises; at its highest point, the vertical velocity is zero. As the object falls towards the Earth again, the vertical velocity increases again in magnitude but points in the opposite direction to the initial vertical velocity.
• The x – and y -motions are recombined to give the total velocity at any given point on the trajectory.

For finding different parameters related to projectile motion, we can make use of differential equations of motions: • For a given launch speed, v0, the max range is at θ= 45.
• For the same v0, launch angles at equal angular increments above and below 45 give (equal) ranges shorter than the max range.
• For each launch speed, v0, and angle θ there is a different parabolic trajectory.

PROJECTILE AT AN ANGLES

• In this case the initial vertical velocity is not zero.
• In order to find initial horizontal and initial vertical we have to resolve into components

ANGLE OF ELEVATION

• Is the angle of projectile trajectory above the horizontal

ANGLE OF DEPRESSION

• Is the angle of projectile trajectory below the horizontal Maximum height

Is the point at which the vertical velocity will be zero above the ground.

PROJECTILE RANGE (R)

• Range is horizontal displacement of a projectile.
• For the projectile launched from the ground the total range will be given by

Horizontal displacement = horizontal velocity x total flight time