Galilean Relativity and Tangential Acceleration

In summary: It's measured in meters per second per second (m/s^2). So, the tangential acceleration is 4 m/s^2 when the instantaneous speed is 4 m/s, and it is -4 m/s^2 when the instantaneous speed is -4 m/s. In summary, Emma swims back and forth a total of 8 times faster across the current than John does.
  • #1
ek
182
0
Any help would be greatly appreciated.

1. Two swimmers, John and Emma, start together at the same point on the bank of a wide stream that flows with the speed c (c>v), relative to the water. John swims downstream a distance L and then upstream the same distance. Emma swims so that her motion relative to the Earth is perpendicular to the banks of the stream. She swims the distance L and then back the same distance, so that both swimmers return to the starting point. Which swimmer returns first?

2. An automobile whose speed is increasing at a rate of .6 m/s^2 travels along a circular road of radius 20m. When the instantaneous speed of the automobile is 4 m/s, what is the tangential acceleration?

Thanks.
 
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  • #2
what is v?

that is the same ether density determining experiment

the swimmer going across would win
 
  • #3
No v value given. Just asking you to solve in terms of time I suppose. Variables only.
 
  • #4
Any help?

Please?
 
  • #5
You were given help.

Her are more details: I assume that v is the speed of the water relative to the shore- you should have said that.

When John swims upstream his speed, relative to the bank, is c- v because he is going against the water. How long will it take him to swim a distance L upstream?
When John swims downstream, his speed, relative to the bank is c+ v because he is carried along by the water. How long will it take him to swim a distance L downstream?
Add those to find the time required to swim both legs.

Since Emma is swimming across the water, she needs to angle slightly up stream. Imagine drawing a line of length vt at an angle upstream, followed by a line of length ct straight down the stream back to the original horizontal. You get a right triangle with hypotenuse of length vt, one leg of length ct, and the other leg of length L, the distance she is swimming. By the Pythagorean theorem, (vt)2= (ct)2+ L2. Solve that for t, the time required to swim the length L across the current. Because she comes back across the current, you can just double that to determine the time necessary to swim both legs.

The second problem is pretty easy. If the speed were constant, the only acceleration would be toward the center of the circle- there would be no "tangential acceleration". Since there is change in speed, the tangential acceleration is precisely that change in speed.
 

1. What is Galilean Relativity?

Galilean Relativity is the idea that the laws of physics are the same in all inertial reference frames. This means that the laws of motion and forces will behave the same way regardless of the observer's perspective or relative velocity.

2. How does Galilean Relativity relate to tangential acceleration?

Galilean Relativity is the foundation for understanding tangential acceleration. Since the laws of motion are the same in all inertial reference frames, tangential acceleration is independent of the observer's frame of reference. This means that the tangential acceleration of an object will be the same regardless of how it is being observed.

3. What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity. It is a measure of how quickly an object's speed is changing along its circular path. This acceleration is always perpendicular to the centripetal acceleration, which is the force that keeps the object moving in a circular path.

4. How is tangential acceleration calculated?

Tangential acceleration can be calculated by taking the derivative of an object's tangential velocity with respect to time. This can be represented by the equation at = dvt/dt = d2s/dt2, where at is the tangential acceleration, vt is the tangential velocity, and s is the displacement of the object along the circular path.

5. What are some real-world applications of Galilean Relativity and tangential acceleration?

Galilean Relativity and tangential acceleration have many practical applications, such as understanding the motion of objects in circular motion, analyzing the forces acting on a rotating object, and predicting the behavior of objects in non-inertial reference frames. This knowledge is crucial in fields such as engineering, astronomy, and physics.

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