How do I do problem number two? I am very confused. Two astronauts have the task

Question

How do I do problem number two? I am very confused.

Two astronauts have the task of gathering visual data about a communications satellite in preparation for a repair. In order to survey the condition of the instruments on the satellite, the two astronauts must position themselves precisely at the right positions as shown below.

The vector that describes astronaut A’s trajectory is defined by the following components:

A: (70 meters, 40 meters)

The magnitude and direction astronaut B’s trajectory is defined by the following magnitude and direction:

B: 80.6 meters at 82.87°

Come to the exploration meeting prepared to answer the following questions:

1) If the ship’s airlock is positioned at the origin of a coordinate plane, what are the components of the vector that takes the astronaut to point B?

2) What is the magnitude and direction of astronaut A’s vector?

3) Given the distance between the astronauts at their respective observation points, what is the maximum cylinder height of the satellite?

4) What vectors describe each astronaut’s path back to the ship?

5) Which astronaut requires the most fuel for their out-and-back maneuver?

Explanation / Answer

consier horizontal axis to the right to eb x axis ( unit vector i) and vertical axis to be y axis( denoted by j)

then

from given data

origin is at ships airlock

a. coordinates of A = 70i + 40j

coorindates of B = 80.6(cos(82.97)i + sin(82.87)j)

components of vector that take astronaut to B are (80.6cos(82.97), 80.6sin(82.97))

=> 9.8645 m, 79.994065 m

b. Magnitude of A = |A| = sqrt(70^2 + 40^2) = 80.622 m

direction = arctan(40/70) = 29.744 deg CCW from +x axis

c. maximum cylinder height = distance between A and B

h = sqrt((70 - 9.8645)^2 + (40 - 79.994)^2) = 72.2204846 m

d. vector of A to come back = -70i - 40j

vector of B to come back = -9.8645i - 79.994065

e. as |A| > |B|

asdtronaut A has to trtavel more distance and hence has to spend more fuel

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.