The magnitude of the displacement is
$\left|\text{\Delta}\overrightarrow{r}\right|=\sqrt{{(4787)}^{2}+{(\mathrm{-11,557})}^{2}}=\mathrm{12,509}\phantom{\rule{0.2em}{0ex}}\text{km}.$ The angle the displacement makes with the
x- axis is
$\theta ={\text{tan}}^{\mathrm{-1}}\left(\frac{\mathrm{-11,557}}{4787}\right)=\mathrm{-67.5}\text{\xb0}.$
Significance
Plotting the displacement gives information and meaning to the unit vector solution to the problem. When plotting the displacement, we need to include its components as well as its magnitude and the angle it makes with a chosen axis—in this case, the
x -axis (
[link] ).
Note that the satellite took a curved path along its circular orbit to get from its initial position to its final position in this example. It also could have traveled 4787 km east, then 11,557 km south to arrive at the same location. Both of these paths are longer than the length of the displacement vector. In fact, the displacement vector gives the shortest path between two points in one, two, or three dimensions.
Many applications in physics can have a series of displacements, as discussed in the previous chapter. The total displacement is the sum of the individual displacements, only this time, we need to be careful, because we are adding vectors. We illustrate this concept with an example of Brownian motion.
Brownian motion
Brownian motion is a chaotic random motion of particles suspended in a fluid, resulting from collisions with the molecules of the fluid. This motion is three-dimensional. The displacements in numerical order of a particle undergoing Brownian motion could look like the following, in micrometers (
[link] ):
In the previous chapter we found the instantaneous velocity by calculating the derivative of the position function with respect to time. We can do the same operation in two and three dimensions, but we use vectors. The instantaneous
velocity vector is now
Let’s look at the relative orientation of the position vector and velocity vector graphically. In
[link] we show the vectors
$\overrightarrow{r}(t)$ and
$\overrightarrow{r}(t+\text{\Delta}t),$ which give the position of a particle moving along a path represented by the gray line. As
$\text{\Delta}t$ goes to zero, the velocity vector, given by
[link] , becomes tangent to the path of the particle at time
t .
a stone is projected from the top of the tower 24.5m high with velocity of 39.2m/s at an angle of 30° with horizontal compute time taken to hit he ground
Suppose the master cylinder in a hydraulic system is at a greater height than the cylinder it is controlling. Explain how this will affect the force produced at the cylinder that is being controlled.
Why is popo less than atmospheric? Why is popo greater than pipi?
Louise
The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.
Louise
David rolled down the window on his car while driving on the freeway. An empty plastic bag on the floor promptly flew out the window. Explain why.
The rate of change in angular displacement is defined as angular velocity.
Manorama
a length of copper wire was measured to be 50m with an uncertainty of 1cm, the thickness of the wire was measured to be 1mm with an uncertainty of 0.01mm, using a micrometer screw gauge, calculate the of copper wire used
if there is a centripetal force it means that there's also a centripetal acceleration, getting back to your question, just imagine what happens if you pull out of a car when it's quickly moving or when you try to stop when you are running fast, anyway, we notice that there's always a certain force..
Lindomar
... that tends to fight for its previous direction when you try to attribute to it an opposite one ou try to stop it.The same thing also happens whe a car goes around a curve, the car it self is designed to a"straight line"(look at the position of its tyres, mainly the back side ones), so...
Lindomar
... whenever it goes around a curve, it tends to throw away its the occupiers, it's given to the fact that it must interrupt its initial direction and take a new one.
When paddling a canoe upstream, it is wisest to travel as near to the shore as possible. When canoeing downstream, it may be best to stay near the middle. Explain why?
one ship sailing east with a speed of 7.5m/s passes a certain point at 8am and a second ship sailing north at the same speed passed the same point at 9.30am at what distance are they closet together and what is the distance between them then