User:Jeff/Physics

(Note to algorithmist.com visitors: I just need to use this page as a sandbox over the weekend... I'll take it down on Monday.)

Part A
The force of gravity that one object exerts on another is equal to G*m1*m2/r^2, where G is a constant, m1 and m2 are the masses of the two objects, and r is the distance between them. On Earth, the acceleration due to gravity equals 9.81 m/s^2. If the mass of Earth is 5.97*10^24 kg, and the radius of the Earth is 6.38*10^6 m, what is the value of G? Be sure to include SI units.

Part B
At what altitude above sea level does the acceleration of gravity become 3% less than the traditional value of 9.81 m/s^2?

Problem 2
At time t=0, a 2.0 kg Jeff awakens to find himself at (0, 0) with an instantaneous velocity of 5.0 m/s in the –î direction. Exactly three forces are acting on Jeff: Fallie = 20 N ∠90°, Fgoogle = 10 N ∠210°, and Fbuttsex. At time t=3.0 s, Jeff's position is (13.5 cos 50° - 15, 13.5 sin 50°).

Part A
If the problem were changed such that Jeff was initially at rest, what would his position have been at time t=3.0 s? Where would he be if V(0) = 5.0 m/s ∠315°?

Part B
Find Jeff's acceleration vector and net force vector.

Part C
Find Fallie,x, Fallie,y, Fgoogle,x, Fgoogle,y, Fnet,x, Fnet,y, and Fbuttsex.

Part D
What was Jeff's position at time t=-1.0 s? What was his instantaneous velocity?

Part E
Let Jeff's instantaneous velocity vector V(t) = Vx(t) î + Vy(t) ĵ. Which of the following is true?
 * Vx(tflip) = 0 for some tflip &gt; 0. The function Vx(t) is increasing.
 * Vy(tflip) = 0 for some tflip &gt; 0. The function Vy(t) is increasing.
 * Vx(tflip) = 0 for some tflip &gt; 0. The function Vx(t) is decreasing.
 * Vy(tflip) = 0 for some tflip &gt; 0. The function Vy(t) is decreasing.

Part F
Find tflip used in part E. What is Jeff's location and velocity at time t=tflip?

Part G
If Fallie disappears at time t=10 s, Fbuttsex goes away at t=20 s, and Fgoogle vanishes at t=30 s, what is Jeff's velocity at t=50 s?

Problem 3
An airplane is flying at a speed of 200 m/s. The airplane releases a package at an altitude of 10 km at time t=0. What is the x-displacement of the package when it hits the ground, if the airplane's velocity is parallel to the x-axis at t=0? If the velocity is parallel to 30°? -45°?