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.)
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- cordinates in MWhich of the following inertial reference frames are proper frames for the two events listed? Choose all that apply. ORED FRAME: A particle traveling at a constant velocity decayed in 3.8 μs. Event A was when. came into being (when it was 'born') & event B was when it decayed (when it 'died'). □ ORANGE FRAME: Event C happened at (5 m, -9 m, -8 m) and event D happened at (-5 m, -0.9 m, -8 m). O YELLOW FRAME: The distance between where event E occurred and where event F occurred was 4 m. □ GREEN FRAME: A rocket was traveling at a constant velocity when it passed through a stationary tunnel. Event G was the front of the rocket entering the tunnel and event H was the the front of the rocket leaving the tunnel. BLUE FRAME: A stationary rocket was engulfed by a hollow cylinder that was moving at a constant velocity. Event J was the front of the rocket entering the cylinder and event K was the the front of the rocket leaving the cylinder.A cosmic ray particle is released from an exploding star that is 2600 Light Years from Earth. If the particle traveled at 98% the speed of light, how far did it travel in its own frame of reference before hitting Earth?
- Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length contraction, where When you multiply the time in a moving frame by γ, you get the longer (dilated) time in your fixed fame. When you divide the length in a moving frame by γ, you get the shorter (contracted) length in your fixed frame. Assume that rocket taxis of the future move about the solar system at half the speed of light. For a 1-hour trip as measured by a clock in the taxi, a driver is paid 10 stellars. The taxi-driver’s union demands that pay be based on Earth time instead of taxi time. If their demand is met, show that the new payment for the same trip would be 11.5 stellars.A laser beam moving at velocity c relative to us is turned on just as three (hypothetical) observers pass by us in the same direction as the beam. Observer 1 has velocity c/2, observer 2 has velocity 0.999c, and observer 3 has velocity c. If metersticks had different lengths in different frames, or clocks ticked at different rates in different frames, it is not impossible that the first and second observers could measure the beam to be moving at speed c relative to them, but the third observer could not find that the beam is moving at speed c relative to her. Prove this quantitavely.A rocket moves with a velocity of 0.832c to the right with respect to a stationary observer A. An observer B moving relative to observer A finds that the rocket is moving with a velocity of 0.940c to the left. What is the velocity of observer B relative to observer A? (Hint: Consider observer B's velocity in the frame of reference of the rocket. Give your answer to three significant figures. Let the positive direction be to the right. Indicate the direction with the sign of your answer.)
- Please derive the Lorentz transformation equations for velocities. For an object, the velocity components seen in reference frame S are: ??, ??, ??. There is a reference frame S’ is moving relative to reference frame S in the direction of +?̂. Derive ?′?, ?′?, ?′?. Please show your derivation details.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.I need help on question 7?
- The space and time coordinates for two events as measured in a frame S are as follows: Event 1: x1=x0 , t1=x0/c Event 2: x2=2x0, t2=x0/2c a. There exists a frame in which these events occur at the same time. Find the velocity of this frame with respect to S. b. What is the value of t at which both events occur in the new frame?You pitch a baseball to your friend from the back of a pick-up truck. You know that you pitch at 40 m/s, but your friend reports that he caught the ball going 10 m/s. What is the speed of the truck? (Use Galilean/Newtonian relativity.For an astronaut traveling to a star 10 lightyears away at v=0.99c and returning, spending negligible amount of time at the destination, describe the journey as the astronaut would observe it. In particular, describe what the astronaut would observe as happening on Earth during the journey