Projectile MotionMotion In Two Dimensions

We restrict ourselves to objects thrown near the Earth’s surface so that gravity can be considered constant.

ObjectiveAt the end of the lesson the learners will be able to :•Investigate the relationship between the projection angle, the height and range of the projectile

Projectile motion refers to the motion of an object that is thrown, or projected into the air at an angle.

The motion of a projectile is determined onlyby the object’s initial velocity and gravity.

Projectile motion applies to sports.

Projectile motion applies to destructiveprojectiles.

Projectile motion is a combination of horizontal motion and vertical motion.  The horizontal motion of a projectile is constant because no gravitational force acts horizontally

The vertical motion of a projectile is nothing more than free fallwith a constant downward acceleration due to gravity.

The vertical motion of a projected object is independent of its horizontal motion.

A projectile moves horizontally with constant velocity while being accelerated vertically. The result is a motionin a curved path.

The path of a projectile is called its trajectory. The trajectory of a projectile in free fall is a parabola.

A projectile, once projected, continues inmotion by its own inertia and is influencedonly by the downward force of gravity.

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.

The cannonball falls the same amount of distance as it did when it was merely dropped from rest

Horizontally launched projectileHorizontal velocity is constant. Vertical velocity is changingdue to gravitational acceleration..

Vertically launched projectileThe horizontal velocity component remains the same size throughout the entire motion of the cannonball.

Projectiles launched at different angles.

Sports Trivia

Maximum range is achieved if the projectile is fired at an angle of 45 degrees with respect to the horizontal.

In ConclusionA projectile is any object thrown horizontally or vertically upon which the only force acting is gravity.

Projectiles travel with a parabolic trajectory due tothe influence of gravity.

There are no horizontal forces acting upon projectilesand thus no horizontal acceleration.

The horizontal velocity of a projectile is constant.there is a vertical acceleration caused by gravity(9.8 m/s).

The horizontal motion of a projectile is independentof its vertical motion.

Relationship between angles and the height:•As the angle increases, the height also increases.

Relationship between the angle and the range:•If the angle is less than 45 degrees, the range is increasing. if the angle is greater than 45 degrees the range is decreasing.

Relationship between the angle and the time:•As the angle increases, the time also increases.

Maximum range is achieved if the projectile is fired at an angle of 45 degrees with respect to horizontal.

In the diagram below, two different possible trajectories are shown for a ball thrown by a center fielder to home plate in a baseball game. Which of the two trajectories, the higher on or the lower one, will result in a longer time for the ball to reach home plate? Explain

Test your knowledge

Suppose a snowmobile is equipped with aflare launcher which is capable of launchinga sphere vertically. If the snowmobile is inmotion and launches the flare and maintains aconstant horizontal velocity after the launch,then where will the flare land (neglect airresistance)?A.On the snowmobile.b. Ahead the snowmobile.C. Behind the snowmobile.

Test your knowledge

Suppose an airplane drops a flare while itis moving at constant horizontal speed atan elevated height. Assuming that air resistance is negligible, where will the flareland relative to the plane?

A. Directly below the plane. B. Below the plane and ahead of it. C. Below plane and behind it.

1. Why does the horizontal component of a projectile’s motion remain constant?2. Why does the vertical component of a projectile’s motion undergo change?3. A projectile is launched vertically at 100 m/s. If air resistance is neglected, at what speed does it return to its initial level?

ASSIGNMENT.

In a long bond paper, draw 2 situations in which you can observe projectile motion and explain each situation.