1. Take a look at the video at this link: https://www.youtube.com/watch?v=hZxCEkGk6HI Ignore air resistance, and consider the time from just after the release until just before impact. What is the acceleration of the piano (magnitude and direction)
(a) just after release, while the piano is travelling upwards?
(b) just before impact with the ground?
(c) right at the top of its trajectory, when its vertical velocity is zero? (You can't see the piano at this point in the video, but you can guess it hasn't stopped to do a hula dance.)
2. The observation deck at the 102nd floor of the Empire State building is 369 meters above the street. If you drop a penny from this height, how long would it take to reach the ground and how fast would it be moving when it hit? Ignore the e↵ects of air resistance (which would actually be significant in this case!)
3. At the SPS Pumpkin Drop, the pumpkins falling from Butte Hall take about 2.1 seconds to reach the ground. What is the height of the stairwell from which they are being dropped?
4. When the pumpkins in the SPS Pumpkin Drop hit the ground, they stop all vertical motion while travelling a distance of 30 cm. Using the fall time from the previous problem, calculate the average acceleration of the pumpkin during the collision with the ground.
5. Alice and Bob are racing. They start together, with an initial speed of zero. Alice accelerates at aA = 5 m/s2 for 1 second, then runs at a constant speed for the remainder of the race. Bob accelerates at aB = 0.6 m/s2 for 9 seconds, then runs at a constant speed for the remainder of the race. (a) Who wins a 100m race, and by what time? (b) Who wins a 5k race, and by what time?
6. A Caparo T1 (a rather ridiculous supercar that none of us will ever get to drive) can go from zero to 100 kilometers per hour in 2.5 seconds. What is the average acceleration during this time?
7. It is theoretically possible1 for a human to throw a golf ball to a height of 16 gira↵es. Given the well-known value of acceleration of gravity on Earth (a = !2.0 gira↵es/s2) what must be the initial speed of this golf ball, in gira↵es/second? Ignore air resistance, because otherwise this problem is tough
8. A car initially at rest accelerates at some acceleration a for a time T, continues at constant velocity for another time T, then accelerates at -2a until it comes to a stop. Sketch the position, velocity, and acceleration graphs for this motion.