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1.A spaceship leaves earth travelling 0.690c. A second spaceship leaves the first at a speed of 0.868c with respect to the first.
a. Calculate the speed of the second ship with respect to the earth if it is fired in the same direction the first spaceship is already moving. Express as a factor of the speed of light.
b. Calculate the speed of the second ship with respect to the Earth if it is fired directly backward toward the Earth. Express as a factor of c.
2.If a spaceship is approaching the earth at 0.17c and a message capsule is sent toward it at 0.21c relative to the earth, what is the speed of the capsule relative to the ship? Answer in c
3.The starship Enterprise leaves a distant earth colony, which is nearly at rest with respect to the earth. The ship travels at nearly constant velocity toward earth. When the Enterprise reaches earth 1.07 y has elapsed, as measured on the ship. Clocks in the earth’s reference frame show that the voyage lasted 3.18 y. How far from earth is the colony, as measured in the reference frame of the earth?
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4.You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem: mass of earth = 5.9742 x 10^24 kg radius of earth = 6.3781 x 10^6 m mass of moon = 7.36 x 10^22 kg radius of moon = 1.7374 x 10^6 m dearth to moon = 3.844 x 10^8 m (center to center) G = 6.67428 x 10^-11 N-m2/kg2 1) On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?
Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as vmin = 11068 m/s. If you leave the surface of the earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully write out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the earth even when the ship is at the surface of the moon!
5.Radiation with a wavelength of 238 nm shines on a metal surface and ejects electrons that have a maximum speed of 3.75×10^5 m/s.
a) How fast must an electron (m = 9.11×10^-31 kg) be moving to have a DeBroglie wavelength of .282 nm?
B) How fast must a neutron (m = 1.67×10^-27 kg) be moving to have a DeBroglie wavelength of .282 nm?
C) How fast must a ball (m = .46 kg) be moving to have a DeBroglie wavelength of .282 nm?
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