Assuming a constant velocity of v=0.87c, how long would the trip to Alpha Centauri take as observed by the ground control team here on Earth?
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

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- 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?You have been posted to a remote region of space to monitor traffic. Near the end of a quiet shift, a spacecraft streaks past. Your laser-based measuring device reports the spacecraft’s length to be 85 m. The identification transponder reports it to be the NCXXB-12, a cargo craft of proper length 100 m. In transmitting your report to headquarters, what speed should you give for this spacecraft?Consider an electron orbiting around a proton with an orbital radius of R=8.48⋅10−10R=8.48⋅10-10 m. What is the orbital frequency of the electron motion? Use me=9.11×10−31me=9.11×10-31 kg, e=1.6×10−19e=1.6×10-19 C, and k=9×109k=9×109 Nm2/C2. The frequency, f0 = Units . By how much would this frequency increase (assume the same orbital radius) if an external magnetic field of B = 0.5 T is applied to the system along the the electron axis of rotation? The increase in the frequency , Δf = Units .
- It takes light from the Sun 6.00 minutes to reach Venus. How far away is the planet from the Sun (in km)? The speed of light, c, is 3 ✕ 105 km/s.Suppose that you are traveling onboard a spacecraft that is moving with respect to the earth at a speed of 0.975c. You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what is your breathing rate?A star has an element in its atmosphere that normally emits a line of frequency fs = 7.5 x 10^14 vib/s. If astronomers measure the frequency of this line to be fo = 7.7 x 10^14 vib/s, then how fast are the Earth and this star traveling relative to each other? Remember that the correct equation for the speed v is given by v = [(fo^2 - fs^2) / (fo^2 + fs^2)] c Remember fo^2 means "fo squared."
- What is the wavelength, in fm (femtometers, or 10^-15 m), of a proton travelling at 90% of the speed of light?An alien spaceship, passing through our solar system, observes us by reflected sunlight from earth’s surface. We know the escape velocity from earth’s surface is vesc = √(2GME/RE). Suppose we can (magically) compress earth radius to a very small size RS so that the escape velocity equals the speed of light c. In that case, nothing, not even light, can escape earth’s gravity and the alien spaceship will observe us as a “dark black hole”! What would be the value of RS? (RS is called the Schwarzschild radius.) a) 8.8 cm b) 8.8 mm c) 8.8 m