1. A cool, hip, skateboarding-type student attempts a fancy manoeuvre. She skates up a ramp, glides through the air and lands smoothly on a second ramp as shown below. Each ramp rises 1 m above the ground and has an angle of 45. The ends of ramps are 3 m apart. With what velocity should she leave the first ramp such that she lands smoothly on the second?

2. Astronomers have discovered a black hole near the star Cygnus-X. Normally a black hole is impossible to see, but the astronomer has noticed the star Cygnus-X orbiting around an invisible, but very massive object. Cygnus-X completes an orbit every 10 earth days. The radius of its orbit is 7.510 11 m. Determine the mass of the black hole.

3. 9. You travel in a spacecraft from Earth to our closest neighbouring star, Proxima Centauri, which is 4.22 ly (light years) away. Your spacecraft travels at 0.9 c.

a. How much time does this take from Earth's frame of reference?

b. How much time does it take from your frame of reference?

c. What distance do you travel from your frame of reference?

d. What distance does an observer from Earth see you traveling?