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Chapter 1: Q19CP (page 39)

2,2,2What is the unit vector in the direction of? What is the unit vector in the direction of3,3,3?

Short Answer

Expert verified

The unit vector in the direction of2,2,2is13,13,13..

The unit vector in the direction of3,3,3is13,13,13. .

Step by step solution

01

Definition of the unit vector

The unit vector in the direction of a vector is the vector divided by its magnitude, which is given by:

r鈬赌=r鈬赌r鈬赌

02

Calculating unit vector for 2,2,2

Take the square root of the sum of the square of each component of the vector2,2,2 to obtain its magnitude,

=22+22+22=23

Divide the vector by its magnitude to compute its unit vector,

r鈬赌=2,2,223=13,13,13

Therefore, the unit vector in the direction of 2,2,2is13,13,13.

03

Calculating unit vector for 3,3,3

Take the square root of the sum of the square of each component of the vector3,3,3 to obtain its magnitude.

=33+33+33=33

Divide the vector by its magnitude to compute its unit vector.

r鈬赌=3,3,333=13,13,13

Therefore, the unit vector in the direction of 3,3,3is13,13,13.

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Most popular questions from this chapter

(a) Apply Newton's first law to each of the following situations. In which situations can you conclude that the object is undergoing a net interaction with one or more other objects? (1) A book slides across the table and comes to a stop. (2) A proton in a particle accelerator moves faster and faster. (3) A car travels at constant speed around a circular race track. (4) A spacecraft travels at a constant speed toward a distant star. (5) A hydrogen atom remains at rest in outer space. (b) A spaceship far from all other objects uses its rockets to attain a speed of. The crew then shuts off the power. According to Newton's first law, which of the following statements about the motion of the spaceship after the power is shut off are correct? (Choose all statements that are correct.) (1) The spaceship will move in a straight line. (2) The spaceship will travel on a curving path. (3) The spaceship will enter a circular orbit. (4) The speed of the spaceship will not change. (5) The spaceship will gradually slow down. (6) The spaceship will stop suddenly.

(a) A unit vector lies in the xy plane, at an angle of 160掳from the +x axis with a positive y component. What is the unit vector? (It helps to draw a diagram). (b) A string runs up and to the left in the xy plane, making an angle of 40掳to the vertical. Determine the unit that points along the string.

Figure 1.60 shows the trajectory of a ball travelling through the air, affected by both gravity and air resistance.

Here are the positions of the ball at several successive times.

Location

t(s)

Position ( m)

A

0.0

(0,0,0)

B

1.0

(22.3,26.1,0)

C

2.0

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a) What is the average velocity of the ball as it travels between location A and location B? b) If the ball continued to travel at the same average velocity during the next second, where would it be at the end of that second? (That is, where would it be at time t=2s )c) How does your prediction from part b) compare to the actual position of the ball at t=2s(location C)? If the predicted and the observed location of the ball are different, explain why?

The crew of a stationary spacecraft observe an asteroid whose mass is4脳1017kg. Taking the location of the spacecraft as the origin, the asteroid is observed to be at location<-3脳103,-4脳103,8脳103>m at a time 18.4s after lunchtime. At a time 21.4s after lunchtime, the asteroid is observed to be at location<-1.4脳103,-6.2脳103,9.7脳103>m. Assuming that the velocity of the asteroid does not change during this time interval, calculate the vector velocityrole="math" localid="1656672441674" v鈫�of the asteroid.

Question: In the periodic table on the inside front cover of this book (or one you find on the internet), for each element there is given the "atomic number," the number of protons or electrons in an atom, and the "atomic mass," which is essentially the number of nucleons, protons plus neutrons, in the nucleus, averaged over the various isotopes of the element, which differ in the number of neutrons. Make a graph of the number of neutrons vs. the number of protons in the elements. You needn't graph every element, just enough to see the trend. What do you observe about the data? (This reflects the need for more neutrons in proton-rich nuclei in order to prevent the electric repulsion of the protons of each other from destroying the nucleus.)
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