Question 1

A spaceship A fires a missile M at velocity $$0.72c ($$relative to A) towards an enemy spaceship E, which is moving away from A at $$0.48c ($$relative to A), as shown in the diagram. What is the velocity of the missile M as observed by the crew on ship E? Use the relativistic velocity addition formula.

Accepted Answer

$$0.37c$$

Question 2

A tank contains a $$1.44\ \mathrm{m}$$ thick layer of oil (index $$n_1 = 1.40$) floating on a 0.96$$\ \mathrm{m}$$ thick layer of brine (index n_2$ = 1.52). A $$ray from the bottom of the tank (point O) reaches the brine-oil interface at the critical angle. What is the horizontal distance from the axis to this point?

Accepted Answer

$$2.3\ \mathrm{m}$$

Question 3

Light of wavelength $$425.0\ \mathrm{nm} in $$air falls at normal incidence on an oil film ($$n = 1.40) of $$thickness $$850.0\ \mathrm{nm}$$ floating on water ($$n = 1.33). $$What is the minimum thickness you should increase the oil film by so that reflected light is canceled (destructive interference)?

Accepted Answer

$$60.7\ \mathrm{nm}$$

Question 4

A laser of wavelength $$514\ \mathrm{nm}$$ passes through a diffraction grating with $$3952$$ lines/cm. If the experiment is performed underwater ($$n = 1.33$$), what is the total number of bright spots observed on the screen?

Accepted Answer

$$13$$

Question 5

A spaceship travels between two space stations $$6.0 	imes 10^7$\ \mathrm{m}$$ apart (in the stations' frame) at $$0.90c. $$How long does the trip take according to an observer on the spaceship? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$97\ \mathrm{ms}$$

Question 6

A relativistic proton has a momentum of $$1.00 	imes 10$$^{-19}$$\ \mathrm{kg \cdot m/s}$$ and a rest energy of $$0.150\ \mathrm{nJ}. $$What is the speed of the proton? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$m_{\mathrm{proton}} = 1.67 	imes 10$$^{-27}$$\ \mathrm{kg})$$

Accepted Answer

$$0.196c$$

Question 7

A relativistic proton has a momentum of $$1.0 	imes 10$$^{-17}$$\ \mathrm{kg \cdot m/s}$$ and a rest energy of $$0.15\ \mathrm{nJ}. $$What is the kinetic energy of this proton? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$m_{\mathrm{proton}} = 1.67 	imes 10$$^{-27}$$\ \mathrm{kg})$$

Accepted Answer

$$3.0\ \mathrm{pJ}$$

Question 8

A stopping potential of $$0.50\ \mathrm{V} is $$required for light of wavelength $$590\ \mathrm{nm} in a $$photoelectric experiment. If the stopping potential for a different wavelength is $$2.30\ \mathrm{V}$$, what is the wavelength of this new light? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$e = -1.60 	imes 10$$^{-19}$$\ \mathrm{C}$$, $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}$$, $$1\ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$\ \mathrm{J})$$

Accepted Answer

$$320\ \mathrm{nm}$$

Question 9

A photon of wavelength $$18.0\ \mathrm{pm} is $$scattered through an angle of $$120^\circ by a $$stationary electron. What is the wavelength of the scattered photon? ($$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}$$, $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$21.6\ \mathrm{pm}$$

Question 10

A hydrogen atom transitions from $$n = 20 to$$ $$n = 5. $$What is the wavelength of the emitted photon? (Ground state energy $$= -13.6\ \mathrm{eV}$$, $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}$$, $$1\ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$\ \mathrm{J}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$2.43\ \mu\mathrm{m}$$

Question 11

A nonrelativistic electron has a kinetic energy of $$5.4\ \mathrm{eV}. $$What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? ($$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$1\ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$\ \mathrm{J})$$

Accepted Answer

$$2.4\ \mathrm{keV}$$

Question 12

A spaceship approaches Earth at $$0.50c. A $$passenger measures his heartbeat as $$70$$ beats per minute. What is his heartbeat rate according to an observer at rest on Earth?

Accepted Answer

$$61$$ beats per minute

Relativistic Velocity Addition: Spaceship and Missile Scenario

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