Answer:
(a) 42.28°
(b) 37.08°
Explanation:
From the principle of refraction of light, when light wave travels from one medium to another medium, we have:
= sinθ
/sinθ
In the given problem, we are given the refractive indices of light which are parallel and perpendicular to the axis of the optical lens as 1.4864 and 1.6584 respectively.
For critical angle θ
= θ
, θ
= 90°; 
(a) 
= sinθ
/sin90°
0.6728 = sinθ![_{c}θ[tex]_{c} = sin^(-1) 0.6728 = 42.28°(b) [tex]n_{a} = 1.6584](https://tex.z-dn.net/?f=_%7Bc%7D%3C%2Fp%3E%3Cp%3E%CE%B8%5Btex%5D_%7Bc%7D%20%3D%20sin%5E%28-1%29%200.6728%20%3D%2042.28%C2%B0%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%28b%29%20%5Btex%5Dn_%7Ba%7D%20%3D%201.6584)
= sinθ
/sin90°
0.60299 = sinθ[tex]_{c}
θ[tex]_{c} = sin^(-1) 0.60299 = 37.08°
Answer:
The magnetic field strength due to current flowing in the wire is9.322 x 10⁻⁶ T.
Explanation:
Given;
electric current, I = 21.3 A
distance of the magnetic field from the wire, R = 45.7 cm = 0.457 m
The strength of the resulting magnetic field at the given distance is calculated as;

Where;
μ₀ is permeability of free space = 4π x 10⁻⁷ T.m/A

Therefore, the magnetic field strength due to current flowing in the wire is 9.322 x 10⁻⁶ T.
Distance= speed * time
So multiply speed and time to get the value of distance
20*9.8 =196 meters
Answer:
The workdone by Jack is 
The workdone by Jill is 
The final velocity is 
Explanation:
From the question we are given that
The mass of the boat is 
The initial position of the boat is 
The Final position of the boat is 
The Force exerted by Jack 
The Force exerted by Jill 
Now to obtain the displacement made we are to subtract the final position from the initial position


Now that we have obtained the displacement we can obtain the Workdone
which is mathematically represented as
The amount of workdone by jack would be

![= [(-420\r i +0\r j +210\r k)(2\r i + 0\r j - \r k)]](https://tex.z-dn.net/?f=%3D%20%5B%28-420%5Cr%20i%20%2B0%5Cr%20j%20%2B210%5Cr%20k%29%282%5Cr%20%20i%20%2B%200%5Cr%20j%20-%20%5Cr%20k%29%5D)



The amount of workdone by Jill would be

![= [(180 \r i + 0\r j + 360\r k)(2\r i +0\r j -\r k)]](https://tex.z-dn.net/?f=%3D%20%5B%28180%20%5Cr%20i%20%2B%200%5Cr%20j%20%2B%20360%5Cr%20k%29%282%5Cr%20i%20%2B0%5Cr%20j%20-%5Cr%20k%29%5D)


According to work energy theorem the Workdone is equal to the kinetic energy of the boat
![W = K.E = \frac{1}{2} m *[v^2 - (1.1)^2]](https://tex.z-dn.net/?f=W%20%3D%20K.E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20m%20%2A%5Bv%5E2%20-%20%281.1%29%5E2%5D)
![-1050 = 0.5*3300 [*v^2- (1.1)^2]](https://tex.z-dn.net/?f=-1050%20%20%3D%200.5%2A3300%20%5B%2Av%5E2-%20%281.1%29%5E2%5D)
![-1050 = 1650 [v^2 -1.21]](https://tex.z-dn.net/?f=-1050%20%3D%201650%20%5Bv%5E2%20-1.21%5D)



