Projectile Motion

Motion In Two DimensionsWe restrict ourselves to objects thrown near the Earths 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 airresistance is negligible.

Describe satellites as fast moving projectiles.

Projectile motion applies to sports.

Projectile motion applies to destructiveprojectiles.

Other ExamplesOfProjectiles

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 onlyby the objects initial velocity, launch angle andgravity.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. 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

In a lot of books you will see the horizontal component called x and the vertical component called y. 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.XY

The x-component of a projectiles motion is there from the start, and stays the same the entire time. The y-component of a projectiles motion doesnt 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 downward acceleration due to gravity.7

A projectile, once projected, continues inmotion by its own inertia and is influencedonly by the downward force of gravity.8, 9Gravity accelerates objects downwards, but is unable to affect the horizontal motion of aprojectile.

A projectile moves horizontally with constant velocity while being accelerated vertically. The result is a motion in a curved path. 10

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 VectorsHorizontal 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 MotionVerticalMotionForces PresentNoYesGravity acting downwardAccelerationPresentNoYesGravity downward at 9.8 m/s2VelocityConstantChanging(by 9.8 m/s each second)

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.

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

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

0, 90minimum range45maximum range Angle with Longest time in Air? 90

Which angle of projection causes a projectile to stay in the air longer? 50 or 70 degrees70 degrees,

(closest to 90, longer time in air)

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

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

Because the verticalvelocity changes by9.8 m/s (in the upward ordownward direction) eachsecond.For example

If a projectile is movingupwards with a velocityof 40 m/s at 0 seconds,then its velocity will be:

30 m/s after 1 second20 m/s after 2 seconds,10 m/s after 3 seconds,40 m/s after 8 seconds.20, 21

Free Fall ResultsHorizontal motion is constantVertical Motion is acceleratedRise time = Fall TimeFinal speed = Initial speed

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

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

In ConclusionA projectile is any object upon which the only forceis 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.

Test your knowledgeSuppose 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)?

Test your knowledgeSuppose 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.

Why does the horizontal component of aprojectiles motion remain constant?Because no force acts on it horizontally.

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

How does the vertical distance a projectilefalls below an otherwise straight-line pathcompare with the vertical distance it wouldfall from rest in the same time?The vertical and horizontal distances areequal.

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. 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? (Neglect air resistance.)

(a)hyperbolic(b)parabolic(c)ellipse(b)parabolic

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 targetExactly at the targetSlightly lower than the target