You are on an interstellar mission from the Earth to the 8.7 light-years distant star Sirius. Your spaceship can travel with 70% the speed of light and has a cylindrical shape with a diameter of 6 m at the front surface and a length of 25 m. You have to cross the interstellar medium with an approximated density of 1 hydrogen atom/m3 . (a) Calculate the time it takes your spaceship to reach Sirius. (b) Determine the mass of interstellar gas that collides with your spaceship during the mission. Note: Use 1.673 × 10−27 kg as proton mass. Considering the effect of time dilation c)how many years will have passed from your perspective?d) at what earth date will you arrive to earth? ( your spaceship launches in june 2020 and returns back to earth directly from sirius)

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dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.

Given the fact that water has less mass per cubic meter than soil and rock , would you expect the value of g to be smaller or larger than average over a lake?

Helpful information: (1) An alpha particle is a helium nucleus, (2) e = 1.6 × 10-¹⁹ C, (3) k₂ = 9.0 × 10⁹ Nm² C-2, (4) 1nm = 1 × 10-⁹ m 1-An alpha particle lies on the x-axis, a distance of 1.0 nanometer from a proton (in this set-up, the alpha particle is at the origin while the proton is in the positive direction). Which of the following choices below represents the magnitude of the electric force on the alpha particle? (a) 2.3 × 10-10 N (b) 4.6 × 10-10 N (c) 2.3 x 10-19 N (d) 4.6 x 10-19 N cing the voltage so following insta choices below at a time! 1.00 s?

Your starship, the Aimless Wanderer, lands on the mysteriousplanet Mongo. As chief scientist-engineer, you make the followingmeasurements: A 2.50 kg stone thrown upward from the ground at12.0 m/s returns to the ground in 4.80 s; the circumference of Mongoat the equator is 2.00 * 10^5 km; and there is no appreciable atmosphereon Mongo. The starship commander, Captain Confusion, asksfor the following information: (a) What is the mass of Mongo? (b) If theAimless Wanderer goes into a circular orbit 30,000 km above the surfaceof Mongo, how many hours will it take the ship to complete one orbit?

Q. 23 : The universal gravitational constant has the dimensions. (a) [M¡ L-3 T²] (b) [m-1 L³ T-²] (c) [M-1 L-3 T] (d) [m' L³ T²]

The mean diameters of planets A and B are 7.3 × 103 km and 1.2 × 104 km, respectively. The ratio of the mass of planet A to that of planet B is 0.41. (a) What is the ratio of the mean density of A to that of B? (b) What is the ratio of the gravitational acceleration on A to that on B? (c) What is the ratio of escape speed on A to that on B?

Three little ducks @ 4 4 crossing a highway at 0.5 mph. The third duckling sees a car coming at 20 mph, but the others are already in the middle of the road. You are the second duckling. What will happen to you and why??