Situation 2- “MY ANKLES ARE BROKEN” (calculations included)
In the world of skiing and snowboarding, there is an infamous gap dubbed Chad’s Gap. A video of Tanner Hall, one of the most renowned professional free-skiers, eating it hard on while attempting to clear it can be seen here, and is best if viewed with audio: http://www.youtube.com/watch?v=2V9h42yspbo. As Tanner makes it quite clear, in his undershooting of the gap, he breaks his ankles. Chad’s gap is approximately 120 feet (36.58 m) wide depending on where you build the jump, and the height difference from the top of the jump to the peak of the landing is around 3m (the landing is lower). This situation relates to projectile motion that we learned in class.
Assuming that the booter (skiing term for the jump built to clear something) is built at a 45 degree angle to the horizontal, it can be determined how fast Tanner should have been going to clear it. The height difference from the booter and the landing should be ignored to account for the fact that momentum towards the landing is lost in the corked (more skiing slang for off center) spins attempted in the jump, as well as air resistance and most importantly the simple fact that by pretending the landing is the same height, your calculations will provide a slight overshooting which is much better than an undershooting (repeat, HIS ANKLES ARE BROKEN, ARGGHHHH). The work for determining how fast he should be going is shown in these pictures taken by my webcam.
Tanner should have been going 26.797 m/s for the sake of his ankles. This seems very fast, but depending on the height of the jump and the amount of snow on the landing, there may be a 3 to 3.5 m difference in height between the jump and the landing, so while 26.797 would be how fast he would have to go to be absolutely sure he gaps it, there is a little bit of a buffer so that he could probably travel slightly slower and still make it. Also, 26.797 m/s may seem very fast, but the world record speed for skiing is 251.4 km/hr, or almost 70 m/s.
Seriously do it on skiing.
You can keep it basic, just the physic of jumping, you have everything you just said. The impact of poping (motion), how important is speed (vectors), gravity, you can draw and explain exemples of parabolic trajectory of peoples jumping, and explain effect of speed/pop (overshoot, undershoot, landing in sweet spot), draw arrows of different colors to show direction of speed and forces. Draw different jumps with different jumps (step-up, step down, table) and explain effect of jump angle (if jump kick or not). Explain/show importance of the landing angle depending on skier's parabolic trajectory. There's also tons of pictures/videos you can use from NS.
You can also go much deeper with trick dynamic and talk about momentum when you pop and effect of inertia while spinning/flipping in the air.