Answer:
The displacement is 6.71 [m} and the angle is 63.4° to the north of east
Explanation:
Using a sketch showing Dante's displacement, we can find each of the points Dante moves through. First, it moves 4 blocks east, the new coordinate (4.0), then moves 3 blocks south and we will get the new coordinate (4, -3). Then Dante moves 1 block west, thus the new point is (3, -3). And finally it moves 9 blocks north where the new coordinate in and gets -3 - (-9) = + 6.
The displacement can be found using the equation for the straight line.
![d= \sqrt{(x_{1}-x_{0} )^{2} +(y_{1}-y_{0} )^{2} } \\d= \sqrt{(3-0 )^{2} +(6-0 )^{2} } \\\\d=6.71 [m]\\](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28x_%7B1%7D-x_%7B0%7D%20%29%5E%7B2%7D%20%2B%28y_%7B1%7D-y_%7B0%7D%20%29%5E%7B2%7D%20%7D%20%5C%5Cd%3D%20%5Csqrt%7B%283-0%20%29%5E%7B2%7D%20%2B%286-0%20%29%5E%7B2%7D%20%7D%20%5C%5C%5C%5Cd%3D6.71%20%5Bm%5D%5C%5C)
We can realize that the triangle formed is a right triangle, therefore we can find the angle of the displacement.
![tan(a)=\frac{6}{3} \\a=tan^-1(2)\\a=63.4[deg]](https://tex.z-dn.net/?f=tan%28a%29%3D%5Cfrac%7B6%7D%7B3%7D%20%5C%5Ca%3Dtan%5E-1%282%29%5C%5Ca%3D63.4%5Bdeg%5D)
It might make more sense putting it another way but this is basically it. you just take the minutes and divide them by 60 to convert them to hours. then simplify the ratio
Answer:
The second material's index of refraction is 1.17.
Explanation:
Given that,
Refractive index of the material, n = 1.29
Critical angle is 65.9 degrees.
We need to find the second material's index of refraction. We know that at critical angle of incidence, angle of refraction is equal to 90 degrees. Using Snell's law as:

So, the second material's index of refraction is 1.17.
Answer:
1 kg
Explanation:
Applying,
Hook's law,
F = ke................. Equation 1
Where F = force, k = force constant of the spring, e = extension.
But from the question,
The weight of the bottle is the force acting on the spring scale
therefore,
mg = ke............ Equation 2
Where m = mass of the bottle, g = acceleration due to gravity.
make k the subject of the equation
k = mg/e............ Equation 3
Given: m = 0.5 kg, e = 1 cm = 0.01 m
Constant: g = 9.8 m/s²
k = (0.5×9.8)/0.01
k = 490 N/m
If the mass of the second bottle is weighed,
given: e = 2 cm = 0.02 m
subtitute into equation 1
m×9.8 = 490×0.02
9.8m = 9.8
m = 9.8/9.8
m = 1 kg.
Hence the mass of the second bottle is 1 kg