Classical Mechanics

Vector Kinematics

Position Vectors

         

A car at point AA on a straight road goes west for 20 20 seconds, arriving at point BB which is 200 200 m away from A.A. The car then heads back to the east for 30 30 seconds, arriving at point CC which is 800 800 m away from B.B. What is the displacement of the car from point AA?

Assume that ++ is east and - is west.

One morning, you wake up and decide to take a jog through the town. You take 54 seconds 54 \text{ seconds} to run 250 m 250 \text{ m} straight north, then you turn right and take 42 seconds 42 \text{ seconds} to run 178 m. 178 \text{ m}. Then you turn right again and run down the street for 9 seconds9 \text{ seconds} covering 30 m 30 \text{ m} until you to stop. Assuming that the coordinates of your home are the origin (0,0),(0, 0), find the position vector of the place where you stop.

Take eastward as +i^ +\hat{i} and northward as +j^. +\hat{j} .

A soccer player undergoes two successive displacements: ΔrA=(28 m)i^+(8 m)j^ followed by ΔrB=(28 m)i^+(7 m)j^. \Delta \vec{r_A} = (28 \text{ m})\hat{i} + (8\text{ m})\hat{j} \text{ followed by } \Delta \vec{r_B} = (-28\text{ m}) \hat{i}+(7\text{ m}) \hat{j}. What is the total displacement of the soccer player?

The motion of a creature in three dimensions can be described by the following equations for positions in x,yx, y and zz directions: x(t)=3t2+6y(t)=t2+3t2z(t)=3t+1.\begin{aligned} x(t)&=3t^2 + 6 \\ y(t)&=- t^2 + 3t - 2 \\ z(t)&= 3t + 1. \end{aligned} Find the position vector of the creature at t=3. t = 3.

The Andromeda galaxy is a giant spiral cluster of stars whose mass is that of 300 300 billion Suns. You can see it with the naked eye as a faint elongated cloud in the night sky. Inasmuch as it subtends an angle of 4.1 4.1^{\circ} and is known to be larger than our own galaxy [163×103 163 \times 10^3 light-years (units of ly) in diameter for Andromeda as compared to 100×103 100 \times 10^3 light-years for our galaxy], how far away is it in light-years?

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