2. Two objects are moving at the same speed of u = 2.25 x 10% ms-1 but in directions perpendicular to each other. Derive the relative speed between the two objects: a) based on the classical, Galilean, velocity transformation formulas; and b) based on the velocity transformation formulas of special relativity.
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- 1. A spaceship A moves east along the x axis with a speed of 0.80c and a spaceship B moves west toward the spaceship A with a speed of 0.70c as measured by an observer on the Earth. Calculate the speed of the spaceship A measured by an observer in the spaceship B in terms of c.1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?1. Taking north as positive and south as negative for all reference frames, suppose Mayor Adams is riding a southbound train to New York City traveling at 40 m/s relative to the ground, while Governor Hochul is riding a northbound train to Albany at 33 m/s relative to the ground. A) What is the velocity of Mayor Adams in Governor Hochul's reference frame (i.e. in the reference frame where Governor Hochul isn't moving)? B) What is the velocity of Governor Hochul in Mayor Adams reference frame? C) To his surprise Mayor Adams observes a groundhog running along the aisle towards the back of the train with a speed of 2 m/s relative to the train. What is the velocity of the groundhog in Governor Hochul's reference frame? D) What is the groundhog's velocity in the reference frame of someone standing at the train station? E) What is its velocity in Mayor Adams's reference frame? F) What is its velocity in the groundhog's frame? 30 10 ft. 5 ft. 15 ft.
- 1) A 5-kg particle's momentum is (211, 329) kg*m/s. Calculate its kinetic energy. 2)Calculate the x-component of vSJ. vS = 6 km/s vJ = 9 km/s θ = 23o 3) In Jupiter's frame, the incoming spacecraft is moving rightward and upward, at 45o. The outgoing spacecraft, having already flown by, is going at the same relative speed, but leftward and upward, also at 45o. (See the figures.) You are going to transform back to the sun's frame and calculate the final outgoing speed. You need to follow several steps: Calculate the vector components of the outgoing vSJ. Add Jupiter's vector velocity to get the outgoing vS. Finally calculate the outgoing speed, vS = |vS| in km/s. Enter that as the final answer. use these parameters: vSJ = 4 km/s vJ = 8 km/s2. Suppose the boat A is moving relative to the water with a velocity of 6 m/s due east and boat B is moving with a velocity of 12 m/s due west. Assume that observers on both boats use reference frames in which the x direction points east. According to the Galilean veloc- ity transformation equations, what is the velocity of boat A relative to boat B. (Hint: Draw a picture. Be sure to define which object corresponds to which frame.)3) The new Earth-Pluto SuperShuttle boasts that it can take you between the two planets, which are 5.0 hours apart in 2.5 hours (according to your watch). What time interval is measured by people in the Earth-Pluto frame? What is the shuttle's speed?
- A newly constructed spaceship has a length of 100.0 m (as measured in the rest frame). This spaceship departs the Earth, bound for a distant planet located a distance D = 50.0 light-years away from the Earth. It travels at a constant speed of v = 0.900c. Part A) As measured by Mission Control on Earth, how long does the journey take? Enter the numerical value in units of years. Part B) According to an astronaut on the spaceship, how long does the journey take? Enter the numerical value in units of years. Part C) As measured by Mission Control on Earth, what is the spaceship's apparent length? Enter the numerical value in SI units1. Some jets emitted by galaxies, for astronomical distances large enough, can appear to travel faster than the speed of light c, through our line of sight. Suppose that a distant galaxy, AB15, is moving with speed v at an angle e with respect to the earth and it emits two light rays separated by a time At in its local time. show that a) The time interval on earth in which the two light rays are emitted is given by Atr = At(1– B cos 0) b) The apparent speed of AB15 measured by an observer on earth is ArT VA = Att B sin e 1-B cos 0 %3D c) For B = 0.75, calculate the value of 0 for which Va =c