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Kinematics in 2-D

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**Review - What is Kinematics???**

Describes the motion of objects Uses a set of equations Draws a relationship between time, distance, velocity, and acceleration

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**We Started in 1-D One dimensional motion (1-D)**

Motion only in one plane (either in the x-direction or the y-direction) Motion in a straight line

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**Now Let’s Do it in 2-D Two Dimensional Motion**

Instead of motion in either the x-direction or the y-direction, we have motion in both the x-direction and the y-direction The motion is no longer in a straight line; it is parabolic

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The Projectile Any object that travels through the air in which the only force acting on it is gravity

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**What are some example of projectiles?**

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And another…

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**Some Important Things to Know**

Projectiles travel in 2 dimensions, in the x-direction AND in the y-direction The ONLY force acting on a projectile is gravity The motion in the x-direction is COMPLETELY INDEPENDENT of the motion in the y-direction…let’s take a look

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**One More Look at Some Projectiles**

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**Sign Conventions Positive directions (+d) Negative directions (-d)**

Right Up Negative directions (-d) Left Down Now it is important as ever!!!

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The Good News… The same equations from 1-D kinematics apply in 2-D

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**Solving Problems Draw a picture of the problem**

Define your sign convention It is your decision, but use one that is convenient Typically, up is positive and right is positive Separate the x-components and the y-components so you can solve them separately Use the GUESS method

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Remember g? Earlier, we said g for the surface of the Earth equals 9.81 m/s2 We were not taking into consideration the direction in which g works What do you think g is?

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Crazy Important… The motion in the x-direction is COMPLETELY INDEPENDENT of the motion in the y-direction There is one link between the x-direction and the y-direction, and it is t

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**Lingo and Such Terms Variables/Constants Projectile Trajectory Range**

Altitude Hang time Vi,x or V0,x Vi,y or V0,y Vf,x Vf,y t d or h g

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Example Problem An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?

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Step 1: Draw a Picture An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?

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Step 1: Draw a Picture Step 2: Define a Sign Convention An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?

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Step 1: Draw a Picture Step 2: Define a Sign Convention Step 3: Pick the direction you want to start in and solve! An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground?

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**Let’s Start in the Y Direction**

An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground? Given: d = m g = -9.8 m/s2 Unknown: t = ? Equation:

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**Let’s Start in the Y Direction**

An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground? Substitute: Solve:

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**to solve the X component**

Now we have what we need to solve the X component

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**Now Let’s Solve the X-Direction**

An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground? Given: vi,x = +115 m/s t = 14.6 sec Unknown: dx = ? Equation:

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**Now Let’s Solve the X-Direction**

An airplane is flying with a constant velocity of 115 m/s. It drops a package from an altitude of 1050 m. If we ignore air resistance, how far down range will the object be when it hits the ground? Substitute: Solve:

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1679 meters

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Practice #1 A car drives off a cliff that is 50 m high. When it lands, investigators measure that the car is 85 m away from the base of the cliff. Calculate the following: the time the car was in the air. the horizontal velocity of the car when it drove off the cliff?

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Practice #2 You throw a ball straight up with an initial vertical velocity of 22 m/s. Calculate the following: the time the ball is in the air. how high the ball goes.

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Objectives: Analyze the motion of an object in free fall. Solve two-dimensional problems. Calculate the range of a projectile.

Objectives: Analyze the motion of an object in free fall. Solve two-dimensional problems. Calculate the range of a projectile.

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