The distance is 30 km and the displacement is 22.4 km North East
The radius of the sphere in meters is ,r = 
Think about the angle the ground and the shadow make. Since the sun's beams are parallel, the angle created by the stick's shadow is also equal. Since the stick is 1 m high and its shadow is 2 m long, we know that the stick's angle is arctan 1/2. Therefore, by thinking of a right-angled triangle,
r/10 = tan [arctan(1/2)] = tan (1/2)
Since, tan (θ/2) = 1-cos(θ) / sin(θ)
we find that,
r/10 = 
Hence, r =
So, the radius of the sphere in meters is ,r =
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Acceleration because it is at a rise in speed. The formula for acceleration is Speed/Time.
The trick here is that there are two variables, Diameter of the coil and number of turns in it. So, in order to solve it, we will need two equations in D and N
Since we are making coil, formula for magnetic field will be B = μₒni/D
D = μₒni/B = 4π x 10^(-7) x (N) x (2.2) / (1.6)x10^(-3) = 1.7 x 10^(-3) x N = D
Another equation will be from the wire's length.
Total length = Circumference of one loop x No. of turns = πD x N = 2.2
We will eliminate N because we need D.
N = 2.2 / πD
Substitute in 1st equation.
1.7 x 10^(-3) x 2.2 / π = D^2
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D = 0.034 m = 3.4 cm </span>
Answer:
Explanation:
a )
Amplitude A = 14 mm , angular frequency ω = 2π / T
= 2π / .5
ω = 4π rad /s
φ₀ = initial phase
Putting the given values in the equation
14 = 25 cos(ωt + φ₀ )
14/25 = cosφ₀
φ₀ = 56 degree
x(t) = 25cos(4πt + 56° )
b )
maximum velocity = ω A
= 4π x 25
100 x 3.14 mm /s
= 314 mm /s
At x = 0 ( equilibrium position or middle point , this velocity is achieved. )
maximun acceleration = ω² A
= 16π² x A
= 16 x 3.14² x 25
= 3943.84 mm / s²
3.9 m / s²
It occurs at x = A or at extreme position.
