Kinematics: Projectile Kinematics: Projectile MotionMotionWhat is Projectile Motion?Characteristics of a Projectile’s TrajectoryHorizontal and Vertical VelocityHorizontal and Vertical Displacement

Projectile MotionProjectile MotionProjectile motion refers to the motion

of an object projected into the air at an angle.◦Eg. A soccer ball begin kicked, a baseball

begin thrown, or an athlete long jumpingThe motion that acts vertically is the

force of gravity, and this pulls an object towards the earth at 9.81 m/s2.

The motion is also moving horizontally but the motion is uniform and constant.

The path of any projectile is a parabola.

Horizontal Motion Vertical Motion

Forces No Yes, the force of gravity acts downward

Acceleration No Yes , "g" is downward at 9.81 m/s2

Velocity Constant Changing (each second the velocity is increasing by 9.81 m/s)

The two motions are The two motions are independent to each other.independent to each other.So an object projected

horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

FormulasFormulasVertical Velocity

◦v2y = v1y+ ay∆t = v1y+ (-9.81m/s2)∆t

Vertical Displacement◦∆dy= v1yi

∆t + 1 ay∆t2 = v1y∆t + 1 (-9.81m/s2)

∆t2

2 2Horizontal Velocity

◦vx = v1x

Horizontal Displacement∆dx = vx∆t

Problem Type 1: No initial vertical velocity (vy1 = 0.0m/s)Once the object leaves the table, it experiences a downward acceleration equal to gravity. Thus the vertical velocity(vy) iscontinually increasing. The horizontal velocity(vx) remains constant and is equal to vx0

. The two vectors vx and vy are

added together to get the velocity at each point on the path.

Problem Type 2: The projectile is launched at an angle

If an object is pointed at an angle, the motion is essentially the same except that there is now an initial vertical velocity(vy0

). Because of the downward acceleration of gravity, vy continually decreases until it reaches its highest point, at which it begins to fall downward.

Initial vertical velocity is equal to: vy1 = v1(sinɵ)

Initial horizontal velocity is equal to: vx1 = v1(cosɵ)

Problem Type 1: Problem Type 1: No initial vertical No initial vertical velocity (vvelocity (vy1y1 = 0.0m/s) = 0.0m/s)

1. A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table's edge and the ball's landing location.

2. A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

Problem Type 2: Problem Type 2: The projectile is The projectile is launched at an anglelaunched at an angle3. A long jumper leaves the ground with an

initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.