Phy Motion question (eng)

2006-12-10 6:44 pm

Marilyn cycles at an average speed of 10.5 m/s
around a circular track in anticlockwise direction from A (Fig).
She stops after 3 minutes. The radius of the circular track is 400m.

Fig:
http://img136.imageshack.us/img136/3044/mathsod6.gif

Q: What is her average velocity?

Ans: 3.14 m/s S45°E

I want to know how to get the answer, please help me ...

回答 (1)

Kwong

2006-12-10 7:40 pm

✔ 最佳答案

Given,
Speed = 10.5 m/s
Time used = 3 min = 180 sec
Radius of Track = 400 m

Therefore, distance travelled = 10.5 x 180 = 1890 m
Since this is an arc length, the movement in angular term is:
1890/400 = 4.725 rad

So the displacement (linear distance between the two points) is:
400 * 2 * sin[(2pi - 4.725)/2]
=562.1073

And velocity = 562.1073/180 = 3.12 m/s

Note (use approximations to the solution):
The angular movement 4.725 rad is close to 270°
If Marilyn start at N, then the stopping point will be at E
Since it is a circular track, the final point is S45°E from starting point.
With a 90° angle of both sides 400m, the displacment is [(400^2) + (400^2)]^(1/2)
= 565.6854 m
Velocity = 3.14 m/s

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