The work done by 
along the given path <em>C</em> from <em>A</em> to <em>B</em> is given by the line integral,
I assume the path itself is a line segment, which can be parameterized by
with 0 ≤ <em>t</em> ≤ 1. Then the work performed by <em>F</em> along <em>C</em> is
![\displaystyle \int_0^1 \left(6x(t)^3\,\vec\imath-4y(t)\,\vec\jmath\right)\cdot\frac{\mathrm d}{\mathrm dt}\left[x(t)\,\vec\imath + y(t)\,\vec\jmath\right]\,\mathrm dt \\\\ = \int_0^1 (288(3t-1)^3-8(2t+5)) \,\mathrm dt = \boxed{312}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cleft%286x%28t%29%5E3%5C%2C%5Cvec%5Cimath-4y%28t%29%5C%2C%5Cvec%5Cjmath%5Cright%29%5Ccdot%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Bx%28t%29%5C%2C%5Cvec%5Cimath%20%2B%20y%28t%29%5C%2C%5Cvec%5Cjmath%5Cright%5D%5C%2C%5Cmathrm%20dt%20%5C%5C%5C%5C%20%3D%20%5Cint_0%5E1%20%28288%283t-1%29%5E3-8%282t%2B5%29%29%20%5C%2C%5Cmathrm%20dt%20%3D%20%5Cboxed%7B312%7D)
T<u>he direction of motion</u> of the person relative to the water is <u>16.7° north of east.</u>
Why?
We can solve the problem by applying the Pitagorean Theorem, where the first speed (to the north) and the second speed (to the east) corresponds to two legs of the right triangle formed with them. (north and east directions are perpendicular each other)
We can calculate the angle that give the direction using the following formula:
Now, substituting the given information we have:
Hence, we have that <u>the direction of motion</u> of the person relative to the water is 16.7° north of east.
Have a nice day!
Answer:
When in free fall, the only force acting upon your body is the force of gravity - a non-contact force. Since the force of gravity cannot be felt without any other opposing forces, you would have no sensation of it. You would feel weightless when in a state of free fall.
Answer:
Explanation:
The equation for this is
where f is the frequency, v is the velocity, and lambda is the wavelength. Filling in:
and
which means that
the wavelength is 1.37 m, rounded to the correct number of significant digits.
Answer:
MATERIAL MEDIUM
Explanation:
Wave is a disturbance that travels through a medium and transfer energy from one point to another without causing any permanent displacement of the medium itself. The two forms of wave are the mechanical wave and the electromagnetic waves.
Mechanical wave is a wave with requires MATERIAL MEDIUM for its propagation. This means that before wave can be propagated at times, material medium is needed e.g a ripple tank. A ripple tank is a mechanical device that generates waves using an instrument called stroboscope attached to it. This kind of wave requires an external source before it can propagate compared to electromagnetic waves that does not require material medium for its propagation.
