Two rockets approach each other. Each is traveling at 0.61c in the earth's reference frame. Part A What is the speed, as a fraction of c, of one rocket relative to the other? ΜΕ ΑΣΦ ? 3 20 F3 % 85 54 $ E R Submit Request Answer Provide Feedback FR t 96 FB & 7 8 9 Y U D F G H J K M 0

An astronaut is traveling in a spacecraft in outer space in a straight line at a constant speed of 0.500c. Which of the following effects would she experience? (a) She would feel heavier, (b) She would find it harder to breath. (c) Her heart rate would change. (d) Some of the dimensions of her spacecraft would be shorter. (e) None of those answers is correct.

An observer in reference frame S sees two events as simultaneous. Event A occurs at the point (50.0 m, 0, 0) at the instant 9:00:00 Universal time, 15 January 2001. Event B occurs at the point (150 m, 0, 0) at the same moment. A second observer, moving past with a velocity of , also observes the two events. In her reference frame S′, which event occurred first and what time elapsed between the events?

An unstable particle with mass m = 3.34 1027 kg is initially at rest. The particle decays into two fragments that fly off along the x axis with velocity components u1 = 0.987c and u2 = 0.868c. From this information, we wish to determine the masses of fragments 1 and 2. (a) Is the initial system of the unstable particle, which becomes the system of the two fragments, isolated or nonisolated? (b) Based on your answer to part (a), what two analysis models are appropriate for this situation? (c) Find the values of for the two fragments after the decay. (d) Using one of the analysis models in part (b), find a relationship between the masses m1 and m2 of the fragments. (e) Using the second analysis model in part (b). find a second relationship between the masses m1 and m2. (f) Solve the relationships in parts (d) and (c) simultaneously for the masses m1 and m2.

An observer in a rocket moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P1.30. The mirror is stationary with respect to S. A light pulse emitted by the rocket travels toward the mirror and is reflected back to the rocket. The front of the rocket is a distance d from the mirror (as measured by observers in S) at the moment the light pulse leaves the rocket. What is the total travel time of the pulse as measured by observers in (a) the S frame and (b) the front of the rocket? Figure P1.30

A rod of length L0 moving with a speed v along the horizontal direction makes an angle 0 with respect to the x axis. (a) Show that the length of the rod as measured by a stationary observer is L = L0[1 (v2/c2)cos2 0]1/2. (b) Show that the angle that the rod makes with the x axis is given by tan = tan 0. These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)

According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 –v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1. (a) For the case of constant F and initial conditions x(0) = 0 = v(0), find x(t) and v(t). (b) Sketch your result for v(t). (c) Suppose that F/m0 = 10 m/s2 ( ≈ g on Earth). How much time is required for the particle to reach half the speed of light and of 99% the speed of light?

An astronaut is traveling in a spacecraft in outer space in a straight line at a constant speed of 0.500c. Which of the following effects would she experience? (a) She would feel heavier. (b) She would find it harder to breathe. (c) Her heart rate would change. (d) Some of the dimensions of her spacecraft would be shorter. (e) None of those answers is correct.

The truck in Figure P39.1 is moving at a speed of 10.0 m/s relative to the ground. The person on the truck throws a baseball in the backward direction at a speed of 20.0 m/s relative to the truck. What is the velocity of the baseball as measured by the observer on the ground? Figure P39.1

An astronaut, of total mass 85.0 kg including her suit, stands on a spherical satellite of mass 375 kg, both at rest relative a nearby space station. She jumps at a speed of 2.56 m/s directly away from the satellite, as measured by an observer in the station. At what speed does that observer measure the satellite traveling in the opposite direction? (See Section 6.2.)