Anonymous at Wed, 16 Oct 2024 07:44:42 UTC No. 16434054

>>16434050
Persons A and B are sitting on a carousel which rotates around the z-axis of K at a constant angular velocity ω relative to a force-free intertial system K. Let K′ be the fixed reference system of the carousel with origin in the center of the carousel, i.e. K′ rotates with ω around the z-axis of K. In this fixed coordinate system, the positions of persons A and
B are given by the time-constant vectors xA = xAe′x and xB = xBe′x with xA > xB. Furthermore, let the basis vectors of K and K′ be identical at time t = 0, i.e. e′αα (0) = eα. Person A aims at an angle ϕ′relative to the negative x′-direction (i.e. ϕ′ = 0 defines the direction to person B) with a billiard cue and accelerates it instantaneously to speed at time t = 0.
Here, D′t is the coordinate derivative in K′
Note: Neglect the rolling motion and friction. Use a computer program for drawing. The following also applies: tan x/2 = sin x/ (1 + cos x), cot x/2 = sin x/ (1 - cos x).
a) Determine the corresponding rotation matrix R with components Rαβ = e′α - eβ and the skew-symmetric matrix Ω = RTR˙ and use it to verify the rotation vector as ω = ωez.

b) What is the initial velocity v0 = v (t = 0) = -v0 cos ϕ ex - v0 sin ϕ ey of the sphere in system K? Determine the coordinates of the trajectory of the sphere in K and K′ as a function of both ϕ and v0 as well as ϕ′ and v′0.

c) Person B is at a distance R from the center of the carousel, while person A is in the center.
sits in the center. Now assume that person A throws the ball so that it flies along the x-axis in the system K.
along the x-axis. Under what conditions will the ball arrive exactly at person B? Draw an example of the possible trajectories.

Anonymous at Wed, 16 Oct 2024 07:48:00 UTC No. 16434057

>>16434054
d) Persons A and B are now sitting opposite each other in the carousel at a distance R from the center, i.e. xA = R and xB = -R. Consider the trajectory curve in K. At what time tR > 0 will the ball in this case be at a distance R from the center of the carousel? Also show that the trajectory satisfies the following transcendental equations in order to get from A to B or A to A:

Anonymous at Wed, 16 Oct 2024 07:49:26 UTC No. 16434058

>>16434050
>>16434054
nicht ein Board für deine Hausaufgabe

Anonymous at Wed, 16 Oct 2024 07:51:36 UTC No. 16434059

a) is quite easy, rotation around z-axis is simple.

i get a problem in b, where he says that the velocity is v_0, and then asks to compute the veocity again? i think he is retarded...

not even that is a problem, in K it is just the derivative of the trajectory

but then c) is the biggest problem. i can easily imagine this happening, but computing is the problem. linear trajectory in K is something like a spiral (2D) in K', but how do i get that as solution?

Anonymous at Wed, 16 Oct 2024 08:33:09 UTC No. 16434076

>>16434058
:(