Answer:
(a) Angle of incidence for violet is more than the angle of incidence for red
(b) 2.4°
Explanation:
refractive index for violet , v = 1.66
refractive index for red, nR = 1.61
wavelength for violet, λv = 400 nm
wavelength for red, λR = 700 nm
Angle of refraction, r = 30°
(a) Let iv be the angle of incidence for violet.
Use Snell,s law
nv = Sin iv / Sin r
1.66 = Sin iv / Sin 30
Sin iv = 0.83
iv = 56°
Use Snell's law for red
nR = Sin iR / Sin r
where, iR be the angle of incidence for red
1.61 = Sin iR / Sin 30
Sin iR = 0.805
iR = 53.6°
So, the angle of incidence for violet is more than red.
(b) iv - iR = 56° - 53.6° = 2.4°
Answer:
The answer to your question is: 15 m/s2
Explanation:
Equation x = at3 - bt2 + ct
a = 4.1 m/s3
b = 2.2 m/s2
c = 1.7 m/s
First we find x at t = 4.1 s
x = 4.1(4.1)3 - 2.2(4.1)2 + 1.7(4.1)
x = 4.1(68.921) - 2.2(16.81) + 6.97
x = 282.58 - 36.98 + 6.98
x = 252.58 m
Now we find speed
v = x/t = 252.58/ 4.1 = 61.6 m/s
Finally
acceleration = v/t = 61.6/4.1 = 15 m/s2
It is given that by using track and cart we can record the time and the distance travelled and also the speed of the cart can be recorded. With all this data we can solve questions on the laws of motion.
Like using the first law of motion we can determine the force of gravity acting on the cart that has moved a certain distance and the velocity or the speed of card has already been registered and since time is known putting the values in formula would help us calculate the gravitational pull acting on cart.
Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
