You go on a round irip in a very fast spacecraft, while your inn in remains behi

Question

You go on a round irip in a very fast spacecraft, while your inn in remains behind on earth (at rest) (Assume that the spacecraft travels at a constant speed, except for the brief turn-around.) Your twin (on Earth) ages 25.00 years while you (on the spacecraft) age only 7.000 years. What was your speed relative to the earth (i.e.. your inn in's frame of reference)? Show your work. Give your final answer as a decimal fraction of c. as of c. using at least 4 significant figures. Do nOT pluR in the numerical value for c! suppose that a high-energy particle accelerates an eletron to such great speed that is relativistic mass becomes as large as the rest mass of a proton. calculate the speed of this electron. show your work. give your final answer as a decimel fraction of c. using at least 8 significant figures. do not plug in numerical value of c! suppose that sound waves with a frequency of a 1.5khz (very high pitch) are normally incedent on a doorway that is 90.cm wide. (let nusound=330m/s in air.) the waves diffract through the doorway. forming a one-slit diffraction patteren. if theta=0 corresponds to the direction normal to the centre of the doorway. at what two angular directions (theta1 and theta2) do the first-order and second-order minima occur,in degree s? show your work completely.

Explanation / Answer

Number 5)

Apply time dilation

T =T'/sqrt(1 - v2/c2)

7/25 = sqrt(1 - v2/c2)

.0784 = 1-v2/c2

.9216 = v2/c2

.9600 = v/c

v = .9600c

Number 6)

Apply m = mo/(sqrt 1 - v2/c2)

1.67 X 10-27 = 9.11 X 10-31/(sqrt 1 - v2/c2)

5.455 X 10-4 = sqrt (1 - v2/c2)

.99999970241995 = v2/c2

v = .99999985c

Number 1)

Apply tan(angle) = m(wavelength)/a

For wavelength, apply v = f(wavelength)

330 = 1500(wavelength)

wavelength = .22 m

tan(angle) = 1(.22)/.9

minima 1 = 13.74o

For the second minima

tan(angle) = 2(.22)/.9

minima 2 = 26.05o

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