College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 26, Problem 56AP

An alien spaceship traveling 0.600c toward Earth launches a landing craft with an advance guard of purchasing agents. The lander travels in the same direction with a velocity 0.800c relative to the spaceship. As observed on Earth, the spaceship is 0.200 light-years from Earth when the lander is launched. (a) With what velocity is the lander observed to be approaching by observers on Earth? (b) What is the distance to Earth at the time of landcr launch, as observed by the aliens on the mother ship? (c) How long does it take the lander to reach Earth as observed by the aliens on the mother ship? (d) If the lander has a mass of 4.00 × 105 kg, what is its kinetic energy as observed in Earth’s reference frame?

(a)

Expert Solution
Check Mark
To determine
The speed of lander approaching observed from Earth.

Answer to Problem 56AP

The speed of lander approaching observed from Earth is 0.946c .

Explanation of Solution

Given Info:

The velocity of the ship relative to Earth is 0.600c .

The velocity of the lander relative to the ship is 0.800c .

Formula to calculate the velocity of the lander relative to Earth is,

vLE=vLS+vSE1+vLSvSEc2

  • vLE is the velocity of the lander relative to Earth
  • vLS is the lander relative to ship
  • vSE is the ship relative to Earth
  • c is the speed of light

Substitute 0.600c for vSE and 0.800c for vLS to find vLE .

vLE=(0.800c)+(0.600c)1+(0.800c)(0.600c)c2=1.40c1.48=0.946c

Thus, the speed of lander approaching observed from Earth is 0.946c .

Conclusion:

The speed of lander approaching observed from Earth is 0.946c .

(b)

Expert Solution
Check Mark
To determine
The distance to Earth when the lander launched as measured by aliens.

Answer to Problem 56AP

The distance to Earth when the lander launched as measured by aliens is 0.160ly .

Explanation of Solution

Given Info:

The proper length between the ship and Earth is 0.200ly .

Formula to calculate the contracted distance measured by observers at rest relative to the spaceship is,

L=Lp1(vSEc)2

  • L is the contracted distance measured by observers at rest relative to the spaceship
  • Lp is the proper length between the ship and Earth

Substitute 0.200ly for Lp and 0.600c for vSE to find L .

L=(0.200ly)1(0.600cc)2=0.160ly

Thus, The distance to Earth when the lander launched as measured by aliens is 0.160ly .

Conclusion:

The distance to Earth when the lander launched as measured by aliens is 0.160ly .

(c)

Expert Solution
Check Mark
To determine
The time taken by the lander to reach Earth as observed by aliens.

Answer to Problem 56AP

The time taken by the lander to reach Earth as observed by aliens is 0.114yr .

Explanation of Solution

Formula to calculate time taken by the lander to reach Earth as observed by aliens is,

t=LvLS+vSE

  • t is the time taken by the lander to reach Earth as observed by aliens

Substitute 0.800c for vLS , 0.600c for vSE and 0.160ly for L to find t .

t=0.160ly(0.800c)+(0.600c) =(0.160ly)(1cyrly)1.40c=0.114yr

Thus, the time taken by the lander to reach Earth as observed by aliens is 0.114yr .

Conclusion:

The time taken by the lander to reach Earth as observed by aliens is 0.114yr .

(d)

Expert Solution
Check Mark
To determine
The kinetic energy of lander as observed in Earth’s reference frame.

Answer to Problem 56AP

The kinetic energy of lander as observed in Earth’s reference frame is 7.51×1022J .

Explanation of Solution

Given Info:

The mass of lander is 4.00×105kg .

The speed of light is 3.00×108m/s .

Formula to calculate The kinetic energy of lander as observed in Earth’s reference frame is,

K.E=(11(vLEc)21)mc2

  • m is the mass
  • K.E is kinetic energy

Substitute 4.00×105kg for m , 3.00×108m/s for c and 0.946c for vLE to find K.E .

K.E=(11(0.946cc)21)(4.00×105kg)(3.00×108m/s)2=7.51×1022J

Thus, kinetic energy of lander as observed in Earth’s reference frame is 7.51×1022J .

Conclusion:

Kinetic energy of lander as observed in Earth’s reference frame is 7.51×1022J

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Chapter 26 Solutions

College Physics

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