Unit 6 Blog - 2D and Projectile Motion Unit

Blog Post – Unit 6 – 2 D motion with projectile motion

Revisit of Free Fall:  We started with revisiting the free fall acceleration model by recalling what we know about objects dropped from rest (v vs. t, displacement from graph, etc) and then considered what would happen when objects are thrown upward.  We tried a Wile E. Coyote problem from the book and drew a motion map showing velocity and acceleration at various times.  Don suggested (a good idea) that we have students draw these vectors approximately to scale, showing how the acceleration vector, when (“multiplied by time to change from acceleration to delta v”) could be added to the previous velocity so that the new velocity could be represented.  This is a challenging idea in straight vector mathematics, but is fairly easy to follow if done graphically.  (I’ve tried this approach previously when dealing with circular motion to show that when acc is multiplied by t we get a new quantity called delta v, which when added to the previous velocity yields the new velocity, which would be in a new direction.  In this way, what’s created is an isosceles triangle since there is no change in overall speed if uniform circular motion. 

  

How to connect new learning to old learning:  consider showing what it would look like if the person were on the ground and kicking the ball at an angle…this would show a full parabola as opposed to just half of a parabola

 

Worksheets:  We spent some time completing some worksheets related to projectile motion and then white-boarded some key results.  Specifically, we attempted to draw a horizontally launched projectile motion problem to scale. 

We then did a practicum in which we attempted to hit a cup with a ball rolled down a ramp and then along a horizontal track.  We then used a pasco launcher to launch at an angle to hit a target.  Having done this lab in the past, history shows that air resistance has a significant effect on the total range. The question is whether or not we should have the students try to take this into account???  This would tend to emphasize practical vs. theoretical. 

Summary of 2D motion:  Horizontal and Vertical Motion of a projectile can be understood by combining and using all previous models (horizontal is CVPM and Free Particle Model), (vertical is CAPM and CFPM)

How I feel about it:  I really like how studying projectile motion after basic forces helps the student understand this difficult topic.  Although students can be (and often are) taught how to solve projectile motion problems without an understanding of forces, incorporating specific aspects of all four previous models should help provide meaningful connections and lead not only to greater conceptual understanding, but I suspect, more concrete problem solving.   For example, the problem of air resistance affecting the path of a projectile can be more easily understood, and described quantitatively if desired, using the forces model. 

How I intend to implement:  I would need to change the order in which I cover topics if I were to cover topics in the same order we did in the workshop.  However, realizing that students really have a difficult time with projectile motion, there is some benefit to covering this topic after forces.  Having said that, it is difficult to do many outdoor activities with projectile motion if the topic is delayed too long in the school year.  At this point in time, I’m uncertain which approach I’ll take.

Difficulties I see coming:   I expect students will still have difficulty solving projectile motion problems as there is a fair amount of mathematical manipulation required, especially if we do angled launches in which vector resolution must also be done.  I am uncertain whether conceptual development (which is the backbone of modeling) will help with problem solving.   I know from experience that a practicum in which students attempt to hit a target from an elevated angled launch position is very difficult to perform; not only in calculation, but also in practice as air resistance can have a significant effect on the projectile’s motion.