Practice problems for Test 1

There is a big hole in the ground which is exactly the same size and shape as this classroom. Your job is to fill the hole with water. I give you an ordinary 12-ounce soda can, which you can fill at a nearby faucet and then pour into the hole.
- Estimate the number of times you must pour a canful of water into the hole in order to fill the hole completely.
- If it takes you 5 seconds to pour each can's worth of water, how many days will it take to fill the hole?
Answer
An asteroid flies through space with an initial velocity of v = (12, -8, 5) km/s. At time t = 0, it is at location p = (400 km, 600 km, -800 km). It is in a region in which the acceleration due to gravity is a = (-2, 0, 3) m/s^2.
- What will the asteroid's position be at time t = 3 minutes?
- What will the asteroid's velocity be at that time?
- What is the asteroid's displacement over this time?
Answer part 1 Answer part 2
Watch the following clip of a Jackie Chan film and figure out how fast Jackie was running as he leapt off the roof of the parking garage.

Click on the image above to watch a Quicktime clip of the jump.

The most chilling stunt in 'Rumble' comes when Jackie, trapped on a rooftop by pursuers, leaps to a balcony on an adjoining building -- a drop of fifteen feet to a three-foot target 26-feet away. "That's a small target," says director Stanley Tong. "You really can't even see where you're aiming before you jump."
After trying the stunt himself with a cable harness, the director concluded that the leap wouldn't look real, and might even be more dangerous if it were done that way.
Instead, he had a 24-foot platform built on the second floor for the star to rehearse on, enabling him to calibrate the exact path he would have to run before leaping. The path was then marked with tape on the roof of the building, and Jackie Chan executed the blind leap with nothing but an airbag to cushion his fall if he missed and fell eight floors to the ground.

So, the questions are:
1. How fast must Jackie have been running when he ran off the parking garage? Assume that his initial velocity was horizontal.
2. The landing area was 3 feet by 3 feet. What was Jackie's margin of error in speed? In other words, how much faster or slower could he have been running and still land on the platform?
Answer part 1 Answer part 2 Answer part 3