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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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What is projectile motion? The only force acting on the objects above is the force of the Earth.

What is projectile motion? The only force acting on the objects above is the force of the Earth.

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