Q. 1 On a pool table ball A with initial velocity VA,i = 1.0iˆm/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 * 1029 kg or 0.08 Msun. 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.