A pregnant woman experiences labor pains, so the husband decided that she will be brought to the nearest hospital, 70 kilometers away. Accordingly, her wife delivered the baby after an hour. Suppose the car that was used to bring the pregnant woman has a speed of 50 km/h. Assume that the speed of light is 60 km/h, will the pregnant woman reach the hospital? Prove your answer with numerical solution.
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- You have an assistantship with a math professor in a future world where space travel is common and spacecraft regularly achieve near-light speeds. A spacecraft has taken off recently to carry individuals to colonize an Earth-like planet around a nearby star. Your professor, who remains on Earth,is teaching the students on the spacecraft via the future version of distance learning. It is time for the students on the spacecraft to take a math exam. The professor wishes the students to have a time interval Δtp = 2.00 h to complete the exam, so just as the spacecraft passes Earth on its last triparound the Sun at its constant cruising speed of 0.960c, she sends a signal to the proctor to have the students begin the exam. Knowing of your experience in physics courses, the professor asks you to determine the time interval through which she should wait before sending a radio signal to thedeparting spacecraft to tell the proctor to have the students stop working on the exam.An alien spaceship travels at v=0.999c-299482km/s (where 'c' is the speed of light equal to 299782 km/s) past the International Space Station (ISS) which orbits the Earth. According to NASA, the ISS is approximately 109m long when they finished building it. What length would the alien spaceship measure? Just under 5m. Just over 200m. The same length, 109m. Just under 100m.Setup: A futuristic trip from Earth to Alpha Centauri is taking place. The travellers start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. a) Team A travels with a constant acceleration so that their worldline can be parametrized by the proper time Tau as t(Tau) = a-1sinh(a*Tau) x(Tau) = a-1(cosh(a*Tau) - 1) for a constant 'a.' They blast off at (t, x) = (0, 0) and travel with this constant acceleration until they reach Alpha Centauri at Earth time of 10 years. What proper time does Team A measure (in years)?
- Observer S detects two flashes of light. A big flash occurs at x1 = 1271 m and, slightly later, a small flash occurs at x2 = 492 m. The time interval between the flashes is Δt = t2 - t1. What is the smallest value of Δt for which observer S' will determine that the two flashes occur at the same x' coordinate?Willy Wonka is in court for running a red light (675 nm). He tells the judge that it was indeed, a green light (540 nm). Calculate how fast Willy Wonka was driving so we can put him in jail in the name of physics.A spacecraft is traveling at ~v = 38.4km s (yes, that is a reasonable speed for a rocket). How long will it take to travel from the earth to the moon, a distance of 384 Mm from Earth?
- Two spaceships, A and B, fly by a space station. An observer on the space station uses a telescope to measure the length of a meterstick in ship A and finds that it is 0.90 m . He does the same for ship B and finds that it is 0.60 m . What is the ratio of the speeds of the two ships relative to the space station, uBuA ?The distance to a particular star, as measured in the earth’s frame of reference, is 7.11 light-years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers on the ship. (a) How long does the trip take, according to observers on earth? (b) What distance for the trip do passengers on the spacecraft measure?A moving spaceship is measured by a stationary observer to have a length that is four-fifths of its proper length. What is the speed v of the spaceship relative to the observer? The speed of light is c = 3.00 × 10³ m/s. U = m/s
- a. What is vav,x for the interval from t = 0 to t = 3.60 s? answer in m/s b. What is vav,x for the interval from t = 0 to t = 3.50 s? anser in m/sSomeone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 years, while an astronaut on the space ship says that the trip took 6.27 years. Find the speed of the spaceship (as measured by someone in Earth's rest frame) in terms of the speed of light. 0.959c 0.687c 0.489c 0.684c 0.779ca) Given a = (7, −6, 4) and b = (3, 8, −1), find a ·b and a ×b.b) A (100 m) long spaceship is travelling at 90% the speed of light. How long is the spaceship as measuredby a stationary observer?