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Images from Shutterstock.com Projectiles What can be asked: The End. 2 Dimensional Kinematics

and Vectors By: Diana Nguyen

AP Physics

Period 5 . One Dim. vs. Two Dim. One dimensional Two dimensional X COMPONENT DON'T FORGET YOUR LIMITS DON'T FORGET YOUR LIMITS RESULTANT VECTOR . . . . Vectors Vector Diagrams Anatomy of a Vector TAIL HEAD works for distance, velocity, force, and acceleration.

once all vectors are places head to tail, the resultant vector can be found Two forces There are two ways to find out the resultant vector when there is only two forces in total. Y COMPONENT The drawing shows a force vector that has a magnitude of 475 newtons. Find the (a) x, (b) y, and (c) z components of the vector. Z = 475*cos(54)

Z = 279.2 N SHADOW = 475*SIN(54)

SHADOW = 384.3 N X = 384.3*cos(33)

X = 322.3 N Y = 384.3*sin(33)

Y = 209.3 N 13 Degrees 38

Degrees 65 Degrees 11 m 10 m 6 m R X Y 11cos13=10.7 11sin13= 2.5 10cos38= -7.9 10sin38= 6.2 6cos65= -2.5 6sin65= -5.4 Rx = .3 Ry = 3.3 Fg = mg Like this apple! Free-body diagram of a projectile A force is required to keep an object in motion. NO! An upward force is not needed to move an object upwards A force is only required to maintain acceleration not motion. In the absence of gravity, an object will follow Newton's law and remain in motion with a same speed and direction. The blue shows the path the ball would take if it was shot horizontally without gravity or dropped. The red is the path that the ball would take with gravity. Notice how the object travels in a parabolic trajectory, due to the influence of gravity. Also notice how gravity never affected the horizontal motion. *Even with gravity, the vertical motion is the only one that is affected, because gravity causes a downward acceleration (in the absence of air resistance). What is a

Projectile Instant in Time Gravity influences the vertical motion of a projectile, this causes a vertical acceleration.

There will be an instant in time where the acceleration is zero. Horizontal motion is the result of the tendency of any object in motion to remain in motion at a constant velocity. Constant velocity means no horizontal acceleration. How high will it go?

How long will it take to get to that height?

What is the total time of flight?

How far will it go? (in x direction) 2 Types of Projectiles 1. Projectile launched from elevated position UNKNOWN: (that you can find)

initial speed

initial height

time flight

horizontal distance 2. Projectile launched at an angle from the horizontal. Rises upwards to a peak, then falls with symmetrical path. UNKNOWN:

time of flight

horizontal distance

height of projectile at peak Dy = 1.6 m Vx = 1100 m/s a = 10 m/s^2 t = ?

Dx = ? Y DIRECTION

Dy = Vi*t + 1/2*a*t^2 Dy = 0 + 1/2*a*t^2 t = = .57 seconds X DIRECTION

Dx = Vi*t + 1/2*a*t^2 Dx = 1100*t

Dx = 1100(.57)

Dx = 627 m Vi = 75 m/s = 60 Degrees = ? Dx = 27 m Vx= 75 cos 60

Vx= 37.5 m/s Vy= 75 sin 60

Vy= 65 m/s X DIRECTION

d = Vi*t + 1/2*a*t^2 27 = 37.5(t)

.72s = t Y DIRECTION

d = Vi*t + 1/2*a*t^2 d = 65(.72) + 1/2(9.8)(.72)^2 d = 65(.72) + 1/2(-9.8)(.72)^2

d = 44.208 m DIRECTION OF A VECTOR PROJECTILE A projectile is an object with only one force action upon it: gravity. It also only has one acceleration: -9.8 m/s^2 .

Any object that is projected or dropped will continue in the motion by it's own inertia and is influenced by nothing else but the downward force of gravity. Misconception: Initial Velocity When people split up vectors, they always think it's a force. Vectors can represent many different type of things. In a projectile object, the only vector that is being split up is initial velocity, IF the projectile is launched at angle. Horizontal Motion

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# AP PHYSICS - Two Dimensional Kinematics and Vectors

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