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

Objectives For a projectile, describe the changes in the horizontal and vertical components of its velocity, when air resistance is negligible. Explain why a projectile moves equal distances horizontally in equal time intervals when air resistance is negligible. Describe satellites as fast moving projectiles.

Projectile motion applies to sports.

Projectile motion applies to destructive projectiles.

Other Examples Of Projectiles

A projectile is any object that moves through the air or through space, acted on only by gravity (and air resistance). The motion of a projectile is determined only by the object’s initial velocity, launch angle and gravity. 1, 2

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 3, 4

The vertical motion of a projected object is independent of its horizontal motion. 5

Let's say a Wiley coyote runs off a cliff Let's say a Wiley coyote runs off a cliff. As he leaves the cliff he has a horizontal velocity. As soon as the coyote leaves the cliff he will experience a vertical force due to gravity.

This force will cause him to start to accelerate in the vertical direction. As he falls he will be going faster and faster in the vertical direction

The horizontal and vertical components of the motion of an object going off a cliff are separate from each other, and can not affect each other. Y X In a lot of books you will see the horizontal component called x and the vertical component called y.

The x-component of a projectile’s motion is there from the start, and stays the same the entire time. The y-component of a projectile’s motion doesn’t even exist at the beginning, but grows bigger as the object falls. 6

The vertical motion of a projectile is nothing more than free fall with a constant acceleration due to gravity. 7

A projectile, once projected, continues in motion by its own inertia and is influenced only by the downward force of gravity. 8

A projectile moves horizontally with constant velocity while being accelerated vertically. The result is a motion in a curved path. 9

Gravity accelerates objects downwards, but is unable to affect the horizontal motion of a projectile. 10

The total distance traveled by a projectile is known as its range. The path of a projectile is called its trajectory.   The trajectory of a projectile in free fall is a parabola. The total distance traveled by a projectile is known as its range. 11, 12, 13

Horizontal Shot. If the barrel of a rifle is horizontal to the surface of the earth when fired, the bullet never rises above the barrel, and gravity causes an immediate descent.

Projectile Vectors Horizontal and vertical components are represented as vectors. 14

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. 15, 16

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

Projectile Motion Summary Horizontal Motion Vertical Motion Forces Present No Yes Gravity acting downward Acceleration Present Gravity downward at 9.8 m/s2 Velocity Constant Changing (by 9.8 m/s each second)

Horizontally launched projectile Horizontal velocity is constant. Vertical velocity is changing due to gravitational acceleration..

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

If projectiles are launched at the same speed, but at different angles, the height and range is of the projectile are affected. 17

Sports Trivia Maximum range is achieved if the projectile is fired at an angle of 45 degrees with respect to the horizontal. 18

0°, 90°minimum range 45°maximum range Angle with Longest time in Air? 90°

70 degrees, (closest to 90, longer time in air) Which angle of projection causes a projectile to stay in the air longer?  50 or 70 degrees 70 degrees, (closest to 90, longer time in air)

http://library.thinkquest.org/27585/lab/sim_pirates.html http://library.thinkquest.org/2779/Balloon.html

If it takes 4 seconds for a projectile to rise to its peak, then it takes 8 seconds to move through the air from start to finish. Why? 19

downward direction) each second. Because the vertical velocity changes by 9.8 m/s (in the upward or downward direction) each second. For example If a projectile is moving upwards with a velocity of 40 m/s at 0 seconds, then its velocity will be: 30 m/s after 1 second 20 m/s after 2 seconds, 10 m/s after 3 seconds, 40 m/s after 8 seconds. 20, 21

Free Fall Results Horizontal motion is constant Vertical Motion is accelerated Rise time = Fall Time Final speed = Initial speed

When the effect of air resistance is significant, the range of a projectile is diminished and the path is not a true parabola. 22

In the case of air resistance, the path of a high-speed projectile falls below the idealized path and follows the solid curve. Computer-generated trajectories of a baseball with and without drag. 23

In Conclusion 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. there is a vertical acceleration caused by gravity (9.8 m/s). The horizontal motion of a projectile is independent of its vertical motion.

Test your knowledge Suppose a snowmobile is equipped with a flare launcher which is capable of launching a sphere vertically. If the snowmobile is in motion and launches the flare and maintains a constant horizontal velocity after the launch, then where will the flare land (neglect air resistance)?

Test your knowledge Suppose an airplane drops a flare while it is moving at constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the flare land relative to the plane? A. Directly below the plane. B. Below the plane and ahead of it. C. Below plane and behind it.

Why does the horizontal component of a projectile’s motion remain constant? Because no force acts on it horizontally.

Why does the vertical component of a projectile’s motion undergo change? Because gravity is pulling it downward.

How does the vertical distance a projectile falls below an otherwise straight-line path compare with the vertical distance it would fall from rest in the same time? The vertical and horizontal distances are equal.

A projectile is launched vertically at 100 m/s A projectile is launched vertically at 100 m/s. If air resistance can be neglected, at what speed does it return to its initial level? 100 m/s

A rock is thrown upward at an angle A rock is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? (Neglect air resistance.) (a) it decreases (b) it increases (c) it remains the same (c) it remains the same

In baseball which path would a home run most closely approximate In baseball which path would a home run most closely approximate? (Neglect air resistance.) (a) hyperbolic (b) parabolic (c) ellipse (b) parabolic

A horizontally traveling car drives off of a cliff next to the ocean A horizontally traveling car drives off of a cliff next to the ocean. At the same time that the car leaves the cliff a bystander drops his camera. Which hits the ocean first? (Neglect air resistance.) (a) car (b) camera (c) they both hit at the same time (c) they both hit at the same time

When a rifle is being aimed at a distant target, the barrel should be lined up so that it points: A. Slightly higher than the target Exactly at the target Slightly lower than the target 