Chapter 31: Q. 60 (page 904)

An $80 k g$ astronaut has gone outside his space capsule to do some repair work. Unfortunately, he forgot to lock his safety tether in place, and he has drifted $5.0 m$ away from the capsule. Fortunately, he has a $1000 W$ portable laser with fresh batteries that will operate it for $1.0 h$ . His only chance is to accelerate himself toward the space capsule by firing the laser in the opposite direction. He has a role="math" localid="1649937737036" $10 - h$ supply of oxygen. How long will it take him to reach safety?

Short Answer

Expert verified

The remaining distance for the Astronaut to travel is $t = 31.533 s \to 8.76 h$ .

Step by step solution

Definition of distance travel:

The distance travelled by a moving object in a given time interval is the length of the object's actual path between its initial and final positions.

Given values:

$c = 3 \times 10^{8} m / s m = 80 k g P = 1000 W t = 1.0 h o u r = 3600 s d = 5.0 m$

Substitute the equation:

After the first hour, the astronaut is traveling the speed of:

$v = \frac{P \cdot t}{m \cdot c}$

$v = \frac{1000 W \times 3600 s}{80 kg \times (3 \times 10^{8} m / s)}$

$v = 1.5 \times 10^{- 4} m / s$

The distance of Astronauts travelled is:

Astronaut has travelled a distance $x$ :

$x = \frac{P}{2 m c} t^{2}$

$x = \frac{1000 W}{2 (80 kg) (3 \times 10^{8} m / s)} (3600 s)^{2}$

role="math" localid="1649938693985" $x = 0.270 m$

Finally, to find the travel remaining distance:

Where $△ x$ is Distance and $v$ is Speed:

$t = \frac{Δ x}{v}$

$t = \frac{5.0 m - 0.270 m}{1.5 \times 10^{- 4} m / s}$

$t = \frac{4.73 m}{1.5 \times 10^{- 4} m / s}$

$t = 31.533 s \to 8.76 h$

Final result:

The result of astronauts remaining distance to travel is $t = 31.533 s \to 8.76 h$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Definition of distance travel:

Given values:

Substitute the equation:

The distance of Astronauts travelled is:

Finally, to find the travel remaining distance:

Final result:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Circular Motion and Gravitation

Force

Fields in Physics

Fundamentals of Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.