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Chapter 1: Q12CP (page 39)

Figure 1.55 shows several arrows representing vectors in the xy plane. (a) Which vectors have magnitudes equal to the magnitude of a炉? (b) Which vectors are equal to a炉?

Short Answer

Expert verified

(a) Vectors c鈬赌,e鈬赌and f鈬赌 have the same magnitude as .

(b) Vectors c鈬赌and f鈬赌are equal to .

Step by step solution

01

Step 1: Magnitude and direction of vectors

While comparing the magnitude of vectors, one can compare the length of the rays.

To check the equality of vectors, both the direction and length of rays must be the same.

02

Finding vectors whose magnitude is the same as a⇀

(a)

By looking at the figure, it is clear that vectorsc鈬赌,e鈬赌 andf鈬赌have the same magnitude as vectora鈬赌. This is because the three rays representing these vectors have the same length as the vectorrole="math" localid="1653919248162" a鈬赌.

Therefore, the vectorsc鈬赌,e鈬赌andf鈬赌have the same magnitude as the vectora鈬赌.

03

Finding vectors equal to  a⇀

(b)

It is evident from the figure that vectorsc鈬赌andf鈬赌have the same direction and magnitude as vectora鈬赌. So, both these are equal to vectora鈬赌.

Therefore, the vectors c鈬赌,f鈬赌 are equal to the vector a鈬赌.

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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.

Question: Which of the following observers might observe something that appears to violate Newton's first law of motion? Explain why. (1) A person standing still on a street corner (2) A person riding on a roller coaster (3) A passenger on a starship traveling at 0.75c toward the nearby star Alpha Centauri (4) An airplane pilot doing aerobatic loops (5) A hockey player coasting across the ice.

Why do we use a spaceship in outer space, far from other objects, to illustrate Newton's first law? Why not a car or a train? (More than one of the following statements may be correct.) (1) A car or train touches other objects, and interacts with them. (2) A car or train can't travel fast enough. (3) The spaceship has negligible interactions with other objects. (4) A car or train interacts gravitationally with the Earth. (5) A spaceship can never experience a gravitational force.

9 An ice hockey puck of mass 170 g enters the goal with a momentum of 鉄�0, 0, 鈭�6.3鉄� kg m/s, crossing the goal line at location 鉄�0, 0,鈭�26鉄� m relative to an origin in the center of the rink. The puck had been hit by a player 0.4 s before reaching the goal. What was the location of the puck when it was hit by the player, assuming negligible friction between the puck and the ice? (Note that the ice surface lies in the xz plane.)

(a) Which of the following do you see moving with constant velocity? (1) A ship sailing northeast at a speed of 5 meters per second (2) The Moon orbiting the Earth (3) A tennis ball traveling across the court after having been hit by a tennis racket (4) A can of soda sitting on a table (5) A person riding on a Ferris wheel that is turning at a constant rate. (b) In which of the following situations is there observational evidence for significant interaction between two objects? How can you tell? (1) A ball bounces off a wall with no change in speed. (2) A baseball that was hit by a batter flies toward the outfield. (3) A communications satellite orbits the Earth. (4) A space probe travels at constant speed toward a distant star. (5) A charged particle leaves a curving track in a particle detector.
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