Answer:
m = 28.7[kg]
Explanation:
To solve this problem we must use the definition of kinetic energy, which can be calculated by means of the following equation.
![E_{k}=\frac{1}{2}*m*v^{2}\\](https://tex.z-dn.net/?f=E_%7Bk%7D%3D%5Cfrac%7B1%7D%7B2%7D%2Am%2Av%5E%7B2%7D%5C%5C)
where:
Ek = kinetic energy = 1800 [J]
m = mass [kg]
v = 11.2 [m/s]
![1800=\frac{1}{2}*m*(11.2)^{2}\\m = 28.7[kg]](https://tex.z-dn.net/?f=1800%3D%5Cfrac%7B1%7D%7B2%7D%2Am%2A%2811.2%29%5E%7B2%7D%5C%5Cm%20%3D%2028.7%5Bkg%5D)
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:
![Tan(\alpha)=\frac{NorthSpeed}{EastSpeed}\\\\Tan(\alpha)^{-1}=Tan(\frac{NorthSpeed}{EastSpeed})^{-1}\\\\\alpha=Tan(\frac{NorthSpeed}{EastSpeed})^{-1}](https://tex.z-dn.net/?f=Tan%28%5Calpha%29%3D%5Cfrac%7BNorthSpeed%7D%7BEastSpeed%7D%5C%5C%5C%5CTan%28%5Calpha%29%5E%7B-1%7D%3DTan%28%5Cfrac%7BNorthSpeed%7D%7BEastSpeed%7D%29%5E%7B-1%7D%5C%5C%5C%5C%5Calpha%3DTan%28%5Cfrac%7BNorthSpeed%7D%7BEastSpeed%7D%29%5E%7B-1%7D)
Now, substituting the given information we have:
![alpha=Tan(\frac{NorthSpeed}{EastSpeed})^{-1}](https://tex.z-dn.net/?f=alpha%3DTan%28%5Cfrac%7BNorthSpeed%7D%7BEastSpeed%7D%29%5E%7B-1%7D)
![\alpha =Tan(\frac{3.6\frac{m}{s} }{12\frac{m}{s} })^{-1}\\\\\alpha =Tan(0.3)^{-1}=16.69\°(North-East)=16.7\°(North-East)](https://tex.z-dn.net/?f=%5Calpha%20%3DTan%28%5Cfrac%7B3.6%5Cfrac%7Bm%7D%7Bs%7D%20%7D%7B12%5Cfrac%7Bm%7D%7Bs%7D%20%7D%29%5E%7B-1%7D%5C%5C%5C%5C%5Calpha%20%3DTan%280.3%29%5E%7B-1%7D%3D16.69%5C%C2%B0%28North-East%29%3D16.7%5C%C2%B0%28North-East%29)
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:
0.173 m.
Explanation:
The fundamental frequency of a closed pipe is given as
fc = v/4l .................. Equation 1
Where fc = fundamental frequency of a closed pipe, v = speed of sound l = length of the pipe.
Making l the subject of the equation,
l = v/4fc ................ Equation 2
also
v = 331.5×0.6T ................. Equation 3
Where T = temperature in °C, T = 18.0 °c
Substitute into equation 3
v = 331.5+0.6(18)
v = 331.5+10.8
v = 342.3 m/s.
Also given: fc = 494 Hz,
Substitute into equation 2
l = 342.3/(4×494)
l = 342.3/1976
l =0.173 m.
Hence the length of the organ pipe = 0.173 m.
Answer:
F = 41,954 N
Explanation:
given,
mass of bucket = 580 Kg
length of the cable = 20 m
velocity = 40 m/s
angle made = 38.0°
T cos 38° = m g..............(1)
T sin 38^0 = \dfrac{mv^2}{l} + F......(2)
dividing equation (2) by (1)
![tan 38^0 = \dfrac{\dfrac{mv^2}{l} + F}{mg}](https://tex.z-dn.net/?f=tan%2038%5E0%20%3D%20%5Cdfrac%7B%5Cdfrac%7Bmv%5E2%7D%7Bl%7D%20%2B%20F%7D%7Bmg%7D)
![tan 38^0 = \dfrac{\dfrac{580\times 40^2}{20} + F}{580 \times 9.81}](https://tex.z-dn.net/?f=tan%2038%5E0%20%3D%20%5Cdfrac%7B%5Cdfrac%7B580%5Ctimes%2040%5E2%7D%7B20%7D%20%2B%20F%7D%7B580%20%5Ctimes%209.81%7D)
![4445.36 = \dfrac{580\times 40^2}{20} + F](https://tex.z-dn.net/?f=4445.36%20%3D%20%5Cdfrac%7B580%5Ctimes%2040%5E2%7D%7B20%7D%20%2B%20F)
F = -46400 + 4445.36
F = -41,954 N
hence, the force is acting in the opposite direction as assumed.
F = 41,954 N