I don’t think kids hate math because its innately boring. I think they hate math becasue we make it boring. We give them stupid word problems about trains leaving two cities at the same time…and who really cares about trains? Give the kids something that they’re actually interested in…
1. Spider-Man is chasing the Green Goblin through New York City. The Green Goblin travels in a straight line, and his Goblin Glider travels at a uniform 40 m/s. Spider-Man travels by webbing. His motion follows a perfect semi-circular arc.
a. If he is to keep up with the Green Goblin, what will his average airspeed equal?
b. What forces are acting on Spider-Man? On the Green Goblin? On Mary Jane?
2. Spider-Man has a mass of 60kg, and is swinging on the end of a 15-meter length of webbing. He starts from rest, and his motion makes an arc equal to 90 degrees of a circle. Ignore air friction and the weight of the webbing and assume the length of the webbing remains constant. Acceleration due to gravity is 9.8 meters per second squared.
a. What is Spider-Man’s maximum velocity?
b. Where will Spider-Man’s velocity be maximzed?
c. Where is he going? Will he get there in time?
3. Venom is at rest, hanging from a crane by a 30-meter length of webbing. Spider-Man has a mass of 60 kg, and Venom has a mass of 120 kg. Spider-Man swings down and collides with him at 30 m/s.
a. Assuming the collision is perfectly elastic, what will be the direction and velocity of Spider-Man and Venom’s vectors, such that kinetic energy and momentum are conserved?
b. Do you think this is a trap?
4. Gwen Stacy is falling off the Brooklyn Bridge (or the George Washington Bridge, depending on who you believe). There is a 50-meter drop to the water below. Gwen Stacy has a mass of 50 kg. Acceleration due to gravity is 9.8 meters per second squared.
a. What is Gwen Stacy’s potential energy at the start of the fall?
b. What is Gwen Stacy’s kinetic energy 5 meters from the water? What is her velocity?
c. If Spider-Man arrests her fall with webbing just before she hits the water, bringing her to rest in 0.5 seconds, how many Newtons of force will be exerted on Gwen Stacy’s neck?
d. Why don’t things ever seem to turn out right for Peter Parker? Why does he seem to hurt people, no matter how he tries not to? Is this the price he must always pay for being…Spider-Man??!
Make sure to show all your work!