Assignment KE and PE Math
Total Score: of 35 points
Directions: Consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. It falls to the ground. Think about the amounts of potential and kinetic energy the bowling ball has:
• as it sits on top of a building that is 40 meters tall.
• as it is half way through a fall off a building that is 40 meters tall and travelling 19.8 meters per second.
• as it is just about to hit the ground from a fall off a building that is 40 meters tall and travelling 28 meters per second.

Questions
(Score for Question 1: ___ of 7 points)
1. Does the bowling ball have more potential energy or kinetic energy as it sits on top of the building? Why?

(Score for Question 2: ___ of 7 points)
2. Does the bowling ball have more potential energy or kinetic energy as it is half way through its fall? Why?

(Score for Question 3: ___ of 7 points)
3. Does the bowling ball have more potential energy or kinetic energy just before it hits the ground? Why?

(Score for Question 4: ___ of 4 points)
4. What is the potential energy of the bowling ball as it sits on top of the building?

(Score for Question 5: ___ of 4 points)
5. What is the potential energy of the ball as it is half way through the fall, 20 meters high?

(Score for Question 6: ___ of 3 points)
6. What is the kinetic energy of the ball as it is half way through the fall?

(Score for Question 7: ___ of 3 points)
7. What is the kinetic energy of the ball just before it hits the ground?

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

it's when something is going so fast it makes a loud noise, breaking the sound barrier, for example: a jet makes a loud noise, not only cause of the jet but because they reached a point where they went so fast that you can year the noise from various parts, kinda like a police car, lets say the car was going   so fast that you hear the siren of the cop car right next to you, but the car is probably a mile a way, it's cos the siren was next to you a few seconds if you understand me