Calculate the momentum vector of the system

Question

Assignment:

Q. 1 On a pool table ball A with initial velocity V_A,_i = 1.0i^ˆm/s collides with ball B which is initially at rest in an elastic collision. The masses of both balls are 0.2 kg, and during the collision ball A is deflected to move at a final velocity 30° from its original direction of motion and a final speed Of 0.866 m/s.

a. Calculate the momentum vector of the system before the collision.

b. Calculate the velocity vector of the ball A after the collision.

c. Calculate the momentum vector of the ball A after the collision.

d. Calculate the velocity vector of the ball B after the collision.

Q. 2 Trappist-1 is a star with 7 exoplanets. The star has a mass of 1.6 * 10^₂₉ kg or  0.08 M_sun. The outermost planet to Trappist-1 (named Trappist-1h) has an orbital period of 18.7 days.

Trappist -1 h is slightly smaller in radius than the Earth (R= 4.9 * 10⁶ m) and its mass is smaller than Earth's (M = 1.97 * 10²⁴ kg).

a. Calculate semi-major axis of Trappist-1 h in AU and in m.

b. Calculate its density.

c. What is a reasonable guess of the composition of Trappist-1 h, based on its density?

d. Calculate the gravitational acceleration of an object near the surface of Trappist-1 h.

e. Calculate the escape speed from the surface of Trappist-1 h.

f. Calculate the moment-of-inertia of Trappist-1. h.

g. Calculate the orbital angular momentum of Trappist-1 h.

h. Calculate the orbital speed of Trappist-1 h.

i. Calculate the kinetic energy of Trappist-1 h.

j. Calculate the orbital energy of Trappist- 1 h.

k. Calculate the kinetic energy of A before the collision.

l. Calculate the kinetic energy of A after the collision.

m. Calculate the kinetic energy of B after the collision.