Physics - Motion 18 (Projectile Motion Review)

OPENING QUESTION: Here are some takeaways from yesterday's formative test:

1) We are ALL comfortable with the idea that we ALWAYS include gravity in calculations involving vertical motion (yay!)

2) Many of us struggle with the idea that the horizontal component of velocity is constant

3) A significant number of folks do not know the equations of motion (ouch!) Please write those down as quickly as you can (GO!)

4) The most difficult part of projectile motion is breaking that motion down into two parts (vertical/horizontal) and analyzing those separately. MOST especially: The total time the object is in the air determines HOW FAR it will go. We will work that hard today!

LEARNING OBJECTIVES:

  • I will create a list of steps for analyzing the motion of an object in projectile motion during today's class.

CALENDAR:

 

WORDS O' THE DAY:

  • Projectile Motion - Up (motion) AND Out (motion)

FORMULAE OBJECTUS:

You MUST know these: MUST MUST MUST MUST MUST

    0) xf = vt

    1) vf = vi +at

    2) vavg = (vi + vf)/2

    3a) xf = xi + vit + 1/2at2

    3b) yf = yi + vit + 1/2at2

    4) vf2 - vi2 = 2a∆x

    4b) vf2 - vi2 = 2a∆y

WORK O' THE DAY:

Here are a whole gaggle of problems (and Solutions):

We'll do the first part together. We're going to be REALLY intentional here and write annotations each step of the way. That's surprisingly difficult to do but also surprisingly helpful!

An object is shot from the ground at an angle of 33.33 degrees to the horizontal with an initial velocity of 24.0 m/s

Have a conversation about what we know about the various characteristics of that object during its entire flight (go!)

Let's discuss!

  • Please sketch and label the situation
  • Please calculate the object's initial horizontal velocity (vix)
  • Please calculate the object's initial vertical velocity (viy)
  • Please calculate how high the object will go (hmax!)
  • Please calculate how much time it will take to get to hmax
  • Please calculate the TOTAL TIME the object will be in flight
  • Now please calculate how far (horizontally) the object will go

My video solution is HERE

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An object is shot from the ground at an angle of 18 degrees to the horizontal with an initial velocity of 34.13 m/s

  • Please sketch and label the situation
  • Please calculate the object's initial horizontal velocity (vix)
  • Please calculate the object's initial vertical velocity (viy)
  • Please calculate how high the object will go (hmax!)
  • Please calculate how much time it will take to get to hmax
  • Please calculate the TOTAL TIME the object will be in flight
  • Now please calculate how far (horizontally) the object will go

My video solution is HERE

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Now let's get a wee bit nasty:

An object is shot from the top of a tower 25 meters above the surrounding ground at an angle of 45.0 degrees to the horizontal with an initial velocity of 49.5 m/s

  • Please sketch and label the situation
  • Please calculate the object's initial horizontal velocity (vix)
  • Please calculate the object's initial vertical velocity (viy)
  • Please calculate how high the object will go (hmax!)
  • Please calculate how much time it will take to get to hmax
  • Please calculate the TOTAL TIME the object will be in flight this is a wee bit trickier
  • Now please calculate how far (horizontally) the object will go

My video solution is HERE

An object is shot from the ground at an angle of 45.0 degrees to the horizontal with an initial velocity of 49.5 m/s but lands in a hole 35.25 meters deep

  • Please sketch and label the situation
  • Please calculate the object's initial horizontal velocity (vix)
  • Please calculate the object's initial vertical velocity (viy)
  • Please calculate how high the object will go (hmax!)
  • Please calculate how much time it will take to get to hmax
  • Please calculate the TOTAL TIME the object will be in flight this is a wee bit trickier
  • Now please calculate how far (horizontally) the object will go

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Imagine you are sitting down to our text next time -- you see a standard projectile motion problem -- which is to say the object is shot, thrown or launched from the ground, experiences projectile motion and then lands on the ground.

  1. How high does it go?
  2. How long does it take to reach hmax?
  3. How far away does it land?

Working solo -- create a bulleted list of the steps you will take to find how far away that object lands

Now I'll move you into groups - Please compare your list with those in your group -- make additions, edits etc...

Imagine you are sitting down to our text next time -- you see a somewhat more difficult projectile motion problem -- which is to say the object is shot, thrown or launched from a height that is different from the height in which it lands.

Working solo -- take a look at your edited/adjusted bulleted list. Which steps will you need to edit for this type of problem?

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Basic Practice:

You launch a grape at an angle of 61 degrees to the horizontal with an initial velocity of 35.2 m/s:

  1. How high does it go?
  2. How long does it take to reach hmax?
  3. How far away does it land?

Video Solution is HERE

Intermediate Practice:

  • You launch a grape at an angle of 33.5 degrees to the horizontal with an initial velocity of 28.27 m/s:
  1. How high does it go?
  2. How long does it take to reach hmax?
  3. How far away does it land?
  • You launch a grape at an angle of 33.5 degrees to the horizontal with an initial vertical velocity of 28 m/s:
  1. How high does it go?
  2. How long does it take to reach hmax?
  3. How far away does it land?

 

Advanced Practice:

  • You launch a grape at an angle of 33.5 degrees to the horizontal with an initial velocity of 28.27 m/s from the top of a 87.50 meter hill:
  1. What is the grapes final altitude?
  2. How long does it take to reach hmax?
  3. How far away does it land?

My Solution is HERE (the screen goes black at the very end when I jump to a website but it comes back!)

  • You launch a grape at an angle of 56 degrees to the horizontal with an initial velocity of 31.23 m/s from the top of a 105 meter hill that lands in the bottom of a 63.5 meter depression:
  1. What is the grapes final altitude?
  2. How long does it take to reach hmax?
  3. How far away does it land?