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PRACTICE：Physics Unit26: Special Theory of Relativity

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Author: physics Total Marks: 61 mks Marks Awarded: _____________

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1#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

You are riding in a spaceship that h:xvow 8 s9gx+z f-1gynas no windows, radios, or other means for you to observe or measure what is outside. You wish to determine if the shipzwy-9 oxgf g:v1+ xn8s is stopped or moving at constant velocity. What should you do?

A. You can determine if the ship is moving by determining the apparent velocity of light.

B. You can determine if the ship is moving by checking your precision time piece. If it's running slow, the ship is moving.

C. You can determine if the ship is moving either by determining the apparent velocity of light or by checking your precision time piece. If it's running slow, the ship is moving.

D. You should give up because you have taken on an impossible task.

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2#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The Michelson-Morley experi/3 ag hu9upavl:ij9+lment was designed to measure

A. the relativistic mass of the electron.

B. the relativistic energy of the electron.

C. the velocity of the Earth relative to the ether.

D. the acceleration of gravity on the Earth's surface.

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3#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Michelson and Morley g3; pah d n4obnx9:z(rconcluded from the results of their experiment that

A. the experiment was a failure since there was no detectable shift in the interference pattern.

B. the experiment was successful in not detecting a shift in the interference pattern.

C. the experiment was a failure since they detected a shift in the interference pattern.

D. the experiment was successful in detecting a shift in the interference pattern.

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4#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

You can build an interferom / m sasbxdd-k fqy75qxms3-/8eter yourself if you use the following components:

A. a light source, a detector screen, a partially silvered mirror, a flat mirror, and a glass plate.

B. a light source, a detector screen, two partially silvered mirrors, and a glass plate.

C. a light source, a detector screen, two partially silvered mirrors, a flat mirror, and a glass plate.

D. a light source, a detector screen, a partially silvered mirror, two flat mirrors, and a glass plate.

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5#

Free-Response ( 1.0 marks) Whole-Paper View Save Problem

State the relativity principle3 p(g8*3 2tuaix rw 18xd.xfz0gbtmoe.

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6#

Free-Response ( 1.0 marks) Whole-Paper View Save Problem

State the three unprovable assumptions of Galilean-Newtonian retj;n 5kob+0g jlativity.

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7#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The theory of special re-/v24g:xwe .2es)7;jv ojra atcvb j slativity

A. is based on a complex mathematical analysis.

B. has not been verified by experiment.

C. does not agree with Newtonian mechanics.

D. does not agree with electromagnetic theory.

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8#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

One of Einstein's postulates in formula9-ph,xfvpos .ting the special theory of relativity was that the laws of physics ar 9o.x-,pf vphse the same in reference frames that

A. accelerate.

B. move at constant velocity with respect to an inertial frame.

C. oscillate.

D. are stationary, but not in moving frames.

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9#

Free-Response ( 1.0 marks) Whole-Paper View Save Problem

State the first postulate o90yka9 s g-j,qqbqzt4 f special relativity.

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10#

Free-Response ( 1.0 marks) Whole-Paper View Save Problem

State the second postula+yv;mrk qtyr. c:lbgc* 5/ 8pwte of special relativity.

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11#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

If you were to measure your pulse rate while in a spaceship moving qcopqrk2* z3o0k.go3 hrux 15away from the Sun at a speed close to the 23zxr .pkcu*qkq3 1hro goo05 speed of light, you would find that it was

A. much faster than normal.

B. much slower than normal.

C. the same as it was here on Earth.

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12#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Relative to a stationary observer, a movin jl8 i6btobwcze-x /,altdv*c79q: o: g clock

A. always runs slower than normal.

B. always runs faster than normal.

C. keeps its normal time.

D. can do any of the above. It depends on the relative velocity between the observer and the clock.

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13#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The gamma factor is defined xqtv) u).kl7 tas $\gamma = 1 / \sqrt{1- (v/c)^2}$, therefore gamma ($\gamma$)

A. can be zero.

B. can be any number less than or equal to one.

C. can be any number greater than or equal to one.

D. cannot equal one.

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14#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Suppose one twin takes a ride in a space ship traveling at a very hig+ny; h8q xe.ymp.ft:8e isx8ph speed to a distant star and back again, while the other twin xym88.: fq i+hpe.tpn 8yse;x remains on Earth. The twin that remained on Earth predicts that the astronaut twin is

A. younger.

B. the same age.

C. older.

D. cannot be determined from the given information

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15#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Relative to a stationa7btg-s:9vo t6i ,lrkt 75u/ rw lmqygr wm*18qry observer, a moving object

A. appears shorter than normal.

B. appears longer than normal.

C. keeps its same length time.

D. can do any of the above. It depends on the relative velocity between the observer and the object.

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16#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

An object moves in a direction paralleljmdy/k 7 s xh,(q7kli* to its length with a velocity that approaches the velocity of light. The width of this object, as measured by y /s7jkh*7mk,ld x(iqa stationary observer,

A. approaches infinity.

B. approaches zero.

C. increases slightly.

D. does not change.

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17#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

An object moves in a q+kl7-)eia (fzy7td n floz87direction parallel to its length with a velocity that approaches the velocity of qenl k7)tz ol+ff 7y7da8zi(-light. The length of this object, as measured by a stationary observer,

A. approaches infinity.

B. approaches zero.

C. increases slightly.

D. does not change.

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18#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

As the speed of a particle approac3c5d/ 3aa0k n j4emz bbik:jj,hes the speed of light, the mass of the partic z43a id03, 5jjkmn:cakbjb/ele

A. increases.

B. decreases.

C. remains the same.

D. approaches zero.

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19#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

As the speed of a particle approaches the speed of light, the momentum of the,pkplx4nk5 8k parkpk5 p,8n4 kxlticle

A. increases.

B. decreases.

C. remains the same.

D. approaches zero.

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20#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A spear is thrown by you at a very high spe)qfi tu5kc5.r ed. As it passes, you measure its length afuc) 5 i.trkq5t one-half its normal length. From this measurement, you conclude that the moving spear's mass must be

A. one-half its rest mass.

B. twice its rest mass.

C. four times its rest mass.

D. none of the given answers

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21#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

What happens to the kinetic energy of a speedy proton when i;v fhb 81)ztqws:hv 0jts relativistic mass doub 8hb : wv1vh;jfq)0stzles?

A. It doubles.

B. It more than doubles.

C. It less than doubles.

D. It must increase, but it is impossible to say by how much.

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22#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

What happens to the total relativistic energy oh;*bl3q 3 zsg)xhr(b-ex g 2obf a speedy proton when its relativistic mass gblb(2)ehxq ;z 3h-x*b3g orsdoubles?

A. It doubles.

B. It more than doubles.

C. It less than doubles.

D. It must increase, but it is impossible to say by how much.

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23#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Consider a particle of massoaw rs5- ga4m1y9vz, ucif24v $m$ and rest mass $m_0$. Which of the following is the correct expression for the kinetic energy of such a particle?

A. $\frac{1}{2} m_0 v^2$

B. $\frac{1}{2} m v^2$

C. $m c^2 - m_0 c^2$

D. $\frac{1}{2}(mc^2 - m_0 c^2)$

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24#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Consider two spaceships, each traveling at 0.50cja6 3lv8yjs z+mjh +3l+mos)l in a straight line. Ship A is moving directly away from the Sun and ship B is approaching th jmhljoljs) 38y m3sv+a6+ z+le Sun. The science officers on each ship measure the velocity of light coming from the Sun. What do they measure for this velocity?

A. Ship A measures it as less than c, and ship B measures it as greater than c.

B. Ship B measures it as less than c, and ship A measures it as greater than c.

C. On both ships it is measured to be less than c.

D. On both ships it is measured to be exactly c.

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25#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Which of the following depends on the observer's 4d20l*mbc5apz: zd hdq 7 w.qcframe of reference?

A. the mass of the proton

B. the length of a meter stick

C. the half-life of a muon

D. all of the given answers

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26#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

As the velocity of your spaceship increases,by(d nyr5d 0md c6v3 lr7t-c+x you would observe

A. that your precision clock runs slower than normal.

B. that the length of your spaceship has decreased.

C. that your mass has increased.

D. all of the given answers

E. none of the given answers

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27#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A boat can travel 4.0 m/s in still water. With what s m2 v,h4a3n ojxe0c0gipeed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is2h,4 am3xvc0gi 0on je heading upstream?

A. 3.0 m/s

B. 4.1 m/s

C. 4.8 m/s

D. 5.0 m/s

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28#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A boat can travel 4.0 m/s in still wa:d 1nvv l ad9c/l3jzk2q0e fjs8o0m6fter. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading downstream6 l9s/ f o18k2:va enjlj0czm0f3qv dd?

A. 3.0 m/s

B. 4.1 m/s

C. 4.8 m/s

D. 5.0 m/s

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29#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A boat can travel 4.0 m/s in still wat4ay,za, )y3qb jny 3pter. With what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/, t,y 334aya)zbjqnyp s if the boat is heading straight across the river?

A. 3.0 m/s

B. 4.1 m/s

C. 4.8 m/s

D. 5.0 m/s

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30#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

How fast should a moving clock travel if it is to be oddv1 kjto ;p8)wkt48v bserved by a stationary observer as running at one-half its normjvd; vtk8kdp8t) w o41al rate?

A. $0.50 \; c$

B. $0.65 \; c$

C. $0.78 \; c$

D. $0.87 \; c$

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31#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A spaceship takes a nonstop journey to a planet and returns in 10 hours accordin80edr ;87yn-zh.e ug u jb8hdyg to a clock on the spacr8g7 - ;.ybuh0dhnue8 zed8 jyeship. If the speed of the spaceship is 0.80c, how much time has elapsed on the Earth?

A. $3.2 \; h$

B. $7.0 \; h$

C. $15 \; h$

D. $17 \; h$

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32#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A set of twins, Andrea and Courtney, are initially 10 years old. Whilq g tf.u.2 f,. 5tjbn0pg4tqw)zhw1ixe Courtney remains on Earth, Andrea rides on a space ship which travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and comes bact0 pif1x gt2zntg, .bw.5uj4qwh q)f .k at 0.6c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

A. $10 \; years$

B. $12 \; years$

C. $18 \; years$

D. $20 \; years$

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33#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

One 20-year-old twin brother takeqn+*4, ah6ddc, yieues a space trip with a speed of 0.80c for 30 years according to a clock on the spaceship. Upon returning to the Earth, what is hise6 eddn4yaq h,* +i,uc own age and the age of the Earth-based twin brother?

A. 20; 30

B. 30; 50

C. 50; 70

D. 70; 90

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34#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A meter stick is moving toward you with a speed of 0.80c. What is its le2kfizkc2)vqa5 4ew ls0e5c:ungth?

A. zero

B. $0.40 \; m$

C. $0.60 \; m$

D. $1.0 \; m$

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35#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

How fast would a rocket ship have to mob0ic;c-twjeob6m+ (z cta v 8*ve to contract to half of its proper length (as observed by a stationa8 0ciw*(b;ca+ j6eztot-v bmcry object)?

A. $0.50 \; c$

B. $0.65 \; c$

C. $0.78 \; c$

D. $0.87 \; c$

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36#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The length of a spaceship ky ha53br-au 9k.jxi9is 10 m when it is at rest. If the spaceship travels by you with a speed of 0.70c, what length does it appear to a99 3b xk5hr-.jkauyi you?

A. $5.5 \; m$

B. $7.1 \; m$

C. $12 \; m$

D. $18 \; m$

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37#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The closest star to our solar system is Alpha Centauri, w u:fbxwp/ t93lqfl 6.frm0/obhich is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels towa q 30tbprf/mf:ol fuw.lx6/b 9rd the star. What distance does the space ship travel according to a passenger on the ship?

A. $2.58 \; ly$

B. $3.52 \; ly$

C. $4.12 \; ly$

D. $4.30 \; ly$

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38#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The closest star to our solar system is Alpha e-kswu 621hss Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much time would elapse on a clock on board the spaceship 12u swk6hss-e?

A. $3.23 \; y$

B. $4.40 \; y$

C. $5.15 \; y$

D. $5.38 \; y$

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39#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The closest star to our solar system is Alpha 7/ fd9k:mfuj:l; lc pwCentauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels cp:l mdj7ku;:9lfwf /toward the star. How much time would elapse on a clock on the Earth?

A. $3.23 \; y$

B. $4.40 \; y$

C. $5.15 \; y$

D. $5.38 \; y$

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40#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

An electron is traveling at 0.85c. What is its f w:yd s:-kix *8uicj:mass? (The rest mass is $9.11 \times 10^{-31} \; kg$.)

A. $1.4 \times 10^{-29} \; kg$

B. $7.2 \times 10^{-30} \; kg$

C. $1.7 \times 10^{-30} \; kg$

D. $2.4 \times 10^{-30} \; kg$

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41#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

What is the speed of a proton if its mass q5 98gxcdc 0mr7qevna /i8f(ab yi8v1 is twice its rest mass?

A. $0.50 \; c$

B. $0.68 \; c$

C. $0.73 \; c$

D. $0.87 \; c$

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42#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

If the velocity of your spaceship goes from 0.3 c to 0.6 9ax9p6p w;gx,1 j fv5t1plleyxkv34jv h 78bvc, then your mass will incr w8j ;9lfjp 9,kvebv61 7p hvp1xx43tx5v ayglease by

A. 19%.

B. 38%.

C. 100%.

D. 200%.

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43#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

What is the momentum lqoeq3 gsgs84.b zpv:me*8l*in $kg \cdot m/s$ of a proton when it is moving with a speed of 0.60c?

A. $1.2 \times 10^{-19} \; kg \cdot m/s$

B. $1.5 \times 10^{-19} \; kg \cdot m/s$

C. $3.0 \times 10^{-19} \; kg \cdot m/s$

D. $3.8 \times 10^{-19} \; kg \cdot m/s$

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44#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

During a reaction, an element loses s/uisli-ln8 rch-r ,5o;7ztg$4.8 \times 10^{-28} \; kg$ of mass. How much energy (in Joules) is released?

A. $4.3 \times 10^{-11} \; J$

B. $1.4 \times 10^{-19} \; J$

C. $1.6 \times 10^{-36} \; J$

D. $5.3 \times 10^{-45} \; J$

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45#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

During a reaction, $1.7 \times 10^{-4} \; J$ of energy is released. What change of mass would cause this?

A. $5.1 \times 10^{-4} \; kg$

B. $1.5 \times 10^{-13} \; kg$

C. $4.8 \times 10^{-18} \; kg$

D. $1.9 \times 10^{-21} \; kg$

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46#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

How much energy would be released if 2.0 kg of ,( v+m ei4ik4rbi4mvapt/ lx0 material was lost during a reaction?a4 pimvx/4 i,t+vr l(bke0i4m

A. $1.8 \times 10^{17} \; J$

B. $1.5 \times 10^{16} \; J$

C. $6.0 \times 10^{8} \; J$

D. $4.7 \times 10^{-8} \; J$

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47#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The amount of energy equivalent to two kilogro fe5;1zh+5-vjxo ; lwnur cq0am of mass at rest is

A. $18 \times 10^{16} \; J$.

B. $3.0 \times 10^{8} \; J$.

C. $9.0 \times 10^{16} \; J$.

D. none of the given answers

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48#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The atomic bomb that was dropped on Naghb io21twlk,/ y4, r,em;piozasaki in 1945 killed 140,000 people, helping to end World War II on the next day. It released energy equivalent to that of 20,000 tons of TNT explosive. How,4/,kh btmi zro1pwye;lo2i , much mass was converted to energy when this took place? (1000 tons of TNT = $4.3 \times 10^{12} \; J$) Incidentally, modern H-bombs have energy yields 1000 times as much!

A. $1 \; g$

B. $10 \; g$

C. $100 \; g$

D. $1 \; kg$

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49#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The kinetic energy of a protoncw(1eicr3xxzc 8-b7 so 8w0p g is 80% of its total energy. What is the speed of the pr z ic78r 0 scw3gp-xcw(1xoeb8oton?

A. $0.02 \; c$

B. $0.87 \; c$

C. $0.98 \; c$

D. $1.0 \; c$

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50#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

The kinetic energy of a proton s zi;v ppai)36is 80% of its total energy. What is the momentum iav6 ip; )pz3sin $kg \cdot m/s$ of the proton?

A. $5.0 \times 10^{-19} \; kg \cdot m/s$

B. $2.5 \times 10^{-19} \; kg \cdot m/s$

C. $5.0 \times 10^{-18} \; kg \cdot m/s$

D. $2.5 \times 10^{-18} \; kg \cdot m/s$

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51#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

What energy is released (in MeV) during a r 7mkw1uk em45k d3(znceaction in which $1.67 \times 10^{-25} \; kg$ of material is converted to energy?

A. $5.0 \times 10^{-14} \; MeV$

B. $4.1 \times 10^{-7} \; MeV$

C. $3.1 \times 10^{-4} \; MeV$

D. $9.4 \times 10^{4} \; MeV$

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52#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

How much mass is lost durinfic )+j3s vhby 0m:r/xg a reaction in which $1.7 \times 10^{8} \; MeV$ of energy is released?

A. $1.8 \times 10^{-8} \; kg$

B. $5.7 \times 10^{-9} \; kg$

C. $1.9 \times 10^{-17} \; kg$

D. $3.0 \times 10^{-22} \; kg$

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53#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

What is the total energy of an electron moving with 1z3m2rxlpte ; a speed of 0.95c?

A. $2.6 \times 10^{-13} \; J$

B. $8.2 \times 10^{-14} \; J$

C. $1.1 \times 10^{-13} \; J$

D. $1.2 \times 10^{-14} \; J$

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54#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

How many joules of energy are required to accelerate one kilogram of mass from r1 tiybz (:72vn;gz )waapv.jgest tojz t) g(paiya nwz2:.1vb;v7g a velocity of 0.866 c?

A. $1.8 \times 10^{17} \; J$

B. $9.0 \times 10^{16} \; J$

C. $3.0 \times 10^{3} \; J$

D. none of the given answers

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55#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

In a nuclear plant, fi fz.z., oopb+ 47bkz$1017$ J of energy is available from mass conversion. How much mass was lost?

A. $0.1 \; kg$

B. $1 \; kg$

C. $10 \; kg$

D. $100 \; kg$

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56#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

An electron is accelerated through 100 kV. By wsb r(t..wue)f hat factor has its mass increased with respectu t..)fwsrb (e to its rest mass?

A. 1.20

B. 1.55

C. 4.25

D. 8.00

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57#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

You are in a rocket traveling aa8ljcy,(- 3nqlcfulz6 gb0zx4 x.0wwway from the Sun at 0.95c. You measure the speed of light from thel-cn6awq8u04 x 3(zflj0cblg.w y,z x Sun to be

A. 0.05c.

B. 0.95c.

C. 1.0c.

D. cannot be determined without knowing the frequency of the light

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58#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

Two spaceships are traveling through space at 0.60 c relative to the Earth. dgcm6i5 i:hz0 If the ships are he :idzh6c5im0g aded directly toward each other, what is their approach velocity, as measured by a person on either craft?

A. $1.2 \; c$

B. $c$

C. $0.60 \; c$

D. none of the given answers

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59#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A fast spaceship is traveling with a speed of g2:r4 2qgtqoe 0.80c. How fast would light travel from the headlights of the ship relative to a stationary obs 2:qqg2 eotgr4erver?

A. $0.20 \; c$

B. $0.80 \; c$

C. $1.0 \; c$

D. $1.8 \; c$

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60#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A spaceship moves away from the Earth with a .;xgxmi0 w dye2 .yx5xspeed of 0.80c. The spaceship then fires a missilg0;.dmx x2xi.wy 5y xee with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth?

A. $0.30 \; c$

B. $0.50 \; c$

C. $0.93 \; c$

D. $1.3 \; c$

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61#

Single-Choice ( 1.0 marks) Whole-Paper View Save Problem

A spaceship moves away from the Earth with a st l2006 ws+ f2mhj9hbn l:rtzrpeed of 0.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measuredt l2lzwb 6 jh09+:2hrt0rmnsf by observers on the Earth if the missile is fired toward the Earth?

A. $0.30 \; c$

B. $0.50 \; c$

C. $0.93 \; c$

D. $1.3 \; c$

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