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A star is located at<6×1010,8×1010,6×1010>m. A planet is located at<-4×1010,-9×1010,6×1010>m. (a) What is the vector pointing from the star to the planet? (b) What is the vector pointing from the planet to the star?

Short Answer

Expert verified

(a) The vector pointing from star to the planet isr→Ps=-10×1010,-17×1010,0m.

(b) The vector pointing from planet to the star isr→Ps=-10×1010,17×1010,0m.

Step by step solution

01

Identification of given data

Star r→s=6×1010,8×1010,6×1010m

Planet r→P=-4×1010,-9×1010,6×1010m

02

Calculating vector pointing from star to planet

(a) Here the tail of the vector will be on the star, and the head of it is on the planet, and the position vector between these two points could be found by subtracting the position of the tail from the position of the head.

r→PS=-4×1010,-9×1010,6×1010-6×1010,8×1010,6×1010r→PS=-10×1010,-17×1010,0

Thus, the required vector is r→PS=-10×1010,-17×1010,0m.

03

Calculating vector pointing from planet to star

(b) The vector pointing from the planet (position of the tail) to the star (position of the head) is the result of subtracting the position of the planet from the position of the star (or simply it is the negative of the position vector from the star to the planet).

r→PS=6×1010,8×1010,6×1010--4×1010,-9×1010,6×1010r→PS=-10×1010,-17×1010,0m=-r→SP

Therefore, the required vector is r→PS=-10×1010,-17×1010,0mm.

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(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 planet is located at <-1×1010,8×1010,-3×1010>. A star is located at <6×1010,-5×1010,1×1010>.

(a)What is r→, the vector from the star to the planet?

(b)What is the magnitude of r→?

(c)What is r^, the unit vector (vector with magnitude 1) in the direction of r→?

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