How I Teach Projectile Motion

For some reason, I find the books totally inadequate on this section.  I also don’t like their method of teaching it.  Our book has one small section and a few problems, but not enough for the kids to see the pattern and understand what’s happening.  I break projectiles into three main parts.

Part 1 – Horizontally Launched Projectiles

The idea here is that a ball is kicked out horizontally with no vertical velocity up or down.  An important concept here is that a ball dropped off a cliff or kicked out horizontally, it will take the same time to fall.  I break these problems into three variations:

1. I give the students the Vx and the height of the cliff and ask them to find the distance horizontally that the ball hits the ground.
2. I give the students the Vx and the distance and ask the students to find the height of the cliff.
3. I give the students the height of the cliff and the distance horizontally that the ball hits the ground and ask them to find the initial velocity.

One the second day we play “Survivor Physics.”  We pick a vocal member of the class and vote him off the airplane.  I draw a picture of him falling and hitting the ground below.  I usually give them the height of the airplane and the speed of the airplane, they have to tell me how long it takes him to fall and how far horizontally he travels before hitting the ground.  Actually I say, “How long does he scream before he goes splat?”  (Problem 1 all over again.)

Next problem, I name a student who drops a water balloon off a building and on to another student.  They get the height of the building and the distance the other student is standing from the bottom of the building.  They need to calculate the horizontal launch velocity.  (Problem 3)

Last, I draw a watch tower and tell them that a student pushes another student off the tower with a certain horizontal velocity.  He has to push him onto a waiting cactus below that is a certain number of meters out.  They need to determine the height of the tower.

Now before you get up in arms over student abuse, understand they are all asking for it to be them that is pushed and thrown and dropped on.  It is all in good fun and they hopefully see a connection to the work.  Hopefully.

Part 2 – Upwardly Launched Projectiles

I teach my students to break these launched projectile problems into two halves; the up half and the down half.  We can solve every problem this way.  The steps are basically the same for every problem.

1. Get Vx and Vy from the velocity and angle.
2. Get the time_up using Vy/g
3. Get the height of the projectile using using 0.5gt^2.
4. Get the total_time by doubling time_up if the projectile lands at the same height it was launched from.
5. Get the distance using d=(Vx)*total_time

Using this method, they can also move the cannon or whatever we launch with up on a hill.  They can then calculate the up time and the down time and see they are different for a different height.  They can also do problems where they determine the height some distance down range by finding out how far an object falls after reaching the maximum height.  These are some of the more tedious projectile problems, but I don’t ease up, they work through them until they get them right.

Part 3 – Unknown Velocity

I was worried my kids wouldn’t be able to solve these problems because you end up with two unknowns and two different equations.  But because the problems are done exactly the same each time, they figured them out fairly quickly.  To solve these, you get the total time like above, just keep a variable for velocity.  Then solve for total time horizontally using Vx and the distance traveled.  Setting them equal to each other lets you get the launch velocity of the projectile.

I know this was a lot of words.  I spend almost two weeks on these problems.  Along the way I take out specifications on military weapons and use those to find the distance they travel.  We use the specs from the Barrett .50 caliber sniper rifle for the horizontal only and upward launch.  The numbers are mind blowing, I find it really gets their interest, especially if any of them are hunters.

The test will be attached below, I need to scan it.