Physics, 17.09.2019 06:30 jaycie16

Acar drives at a constant speed around a banked circular track with a diameter of 136 m . the motion of the car can be described in a coordinate system with its origin at the center of the circle. at a particular instant the car's acceleration in the horizontal plane is given by a⃗ =(−15.4i^−25.4j^)m/s2.
what is the car's speed?
where (x and y) is the car at this instant?

Answers: 3

Show answers

Answers

Answer from: bonetanne7171

speed = 44.9m/s

x = 35.5 m, y = 58.0m

Explanation:

A car on a circular track with constant angular velocity ω can be described by the equation of position r:

$\overrightarrow {r(t)} = Rsin(\omega t)\hat{i} + Rcos(\omega t)\hat{j}$

The velocity v is given by:

$\overrightarrow {v(t)} = \overrightarrow{\frac{dr}{dt}}= \omega Rcos(\omega t)\hat{i} - \omega Rsin(\omega t)\hat{j}$

The acceleration a:

$\overrightarrow {a(t)} = \overrightarrow{\frac{dv}{dt}}= -\omega^2 Rsin(\omega t)\hat{i} - \omega^2 Rcos(\omega t)\hat{j}$

From the given values we get two equations:

$-\omega^2 Rsin(\omega t)=-15.4\\-\omega^2 Rcos(\omega t)=-25.4$

We also know:

$\overrightarrow {a(t)} = -\omega^2 Rsin(\omega t)\hat{i} - \omega^2 Rcos(\omega t)\hat{j}=-\omega^2\overrightarrow{r(t)}$

The magnitude of the acceleration a is:

$a=\sqrt{(-15.4)^2+(-25.4)^2}=29.7$

The magnitude of position r is:

r=R=68m

Plugging in to the equation for a(t):

$\overrightarrow {a(t)} =-\omega^2\overrightarrow{r(t)}$

and solving for ω:

$|\omega|=0.66$

Now solve for time t:

$\frac{sin(0.66t)}{cos(0.66t)}=tan(0.66t)=\frac{15.4}{25.4}\\t=0.83$

Using the calculated values to compute v(t):

$\overrightarrow {v(t)}= \omega Rcos(\omega t)\hat{i} - \omega Rsin(\omega t)\hat{j}\\\overrightarrow {v(t)}=44.88cos(0.55)\hai{i}-44.88sin(0.55)\hat{j}\\\overrightarrow {v(t)}=38.3\hat{i}-23.5\hat{j}$

The speed of the car is:

$\sqrt{38.3^2 + (-23.5)^2} = 44.9$

The position r:

$\overrightarrow {r(t)} = Rsin(\omega t)\hat{i} + Rcos(\omega t)\hat{j}\\\overrightarrow {r(t)} = 68sin(0.55)\hat{i} + 68cos(0.55)\hat{j}\\\overrightarrow {r(t)} = 35.5{i} + 58.0\hat{j}$

Answer from: yyy77uh

v = 44.9 m/s

x = 68 cos58.77 = 35.25 m

y = 68 sin58.77 = 58.14 m

Explanation:

As we know that car drives at constant speed along circular path then we will have its position vector given as

$\vec r = R cos\omega t \hat i + R sin\omega t \hat j$

now if we differentiate is with respect to time then it will give as instantaneous velocity

so we have

$v = -R\omega sin\omega t \hat i + R\omega cos\omega t\hat j$

now again its differentiation with respect to time will give us acceleration

$a = - R \omega^2 cos\omega t \hat i - R\omega^2 sin\omega t\hat j$

now if we compare it with given value of acceleration

$a = -15.4\hat i - 25.4 \hat j$

$R\omega^2cos\omega t = 15.4$

$R\omega^2sin\omega t = 25.4$

divide both equations then we will have

[tec]tan\omega t = 1.65[/tex]

$\omega t = 58.77 degree$

Now we have

R = 68 m/s

so we can solve it for

$R\omega^2cos58.77 = 15.4$

$\omega = 0.66 rad/s$

so speed of the car is given as

$v = R\omega$

$v = 0.66\times 68$

v = 44.9 m/s

now we have coordinates of car given as

$x = R cos\omega t$

x = 68 cos58.77 = 35.25 m

$y = R sin\omega t$

y = 68 sin58.77 = 58.14 m

Answer from: Quest

first thing first of the answer is with technology. second thing second thing is that the big bang theory did not happened u see they say it did but what they dont realize is that like dinasures are still a round they might deny it but they and look at these 12 foot human skelteons they find lets see didnt the bible say something about giants. hope this peace.

Answer from: Quest

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol

b. a hockey puck sliding across the ice

c. a compressed spring

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice is the correct option.

Another question on Physics

Physics, 21.06.2019 22:50

Two horizontal plates with infinite length and width are separated by a distance h in the z direction. the bottom plate is moving at a velocity u. the incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. align gravity with positive z. assume that the flow is fully-developed and laminar. if the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. sketch your system 2. identify the coordinate system to be used. 3. show your coordinates and origin point on the sketch. list all your assumptions. 5. apply the continuity equation to your system. nts of navier stokes equations of choice to your system 7. solve the resulting differential equation to obtain the velocity profile within the system make sure to list your boundary conditions. check units of velocity 8. describe the velocity profile you obtain using engineering terminology. sketch that on the same sketch you provided in (1). 9. obtain the equation that describes the volumetric flow rate in the system. check the units.

Answers: 2

Answer

Physics, 22.06.2019 00:30

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

Answers: 2

Answer

Physics, 22.06.2019 03:30

What elements are found in the inner and out core of the earth? the correct layers of earth's interior from the top to the center? what is the unwanted material that is removed from a mine called? how much stronger is an earthquake that registers 5 on the richter as opposed to 2? what occurs at a convergence plate boundary? the majority of the the earth's rock what is the most common element found in the earth's crust? what element is found in pyrite that contributes to acid mine drainage? why must mining companies post bond prior to permitting? how are bacteria being used in treating effluent from mines? what is a problem of acid mine drainage in rivers and soils? what do tectonic plates move on? why is gold smelting so damaging? how are artesian wells formed? where is dammed water colder than the river it flows into? what is one of the problems of uncontained aqueducts? what is the largest use of industrial water? underground sand and gravel formations that can store water? what type of water test measure acidity? which type of water test for cloudiness from suspended solids? what water test measures the amount of calcium and magnesium? these are all problems of coal power plants all of the following are advantages of riparian lands along rivers what type of water would be the warmest and have the least amount of dissolved oxygen? the zone of aeration is

Answers: 1

Answer

Physics, 22.06.2019 13:10

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)

Answers: 2

Answer

You know the right answer?

Acar drives at a constant speed around a banked circular track with a diameter of 136 m . the motion...

Questions