Explanation:
An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is given by :
Where
s is in centimeters
t is in seconds
Velocity of the particle,
Acceleration of the particle,
Hence, this is the required solution.
Most likely it will reflect off the surface and create a fire
Refer to the figure shown below.
Let V = speed of the boat relative to the water
Given:
u = 1 km/h the speed of flowing water.
When traveling downstream from A to B, the actual speed of the boat is
V₁ = V + u = V + 1 km/h
When traveling upstream from B to A, the actual speed of the boat is
V₂ = V - u =V - 1 km/h
Because the distance Ab is 1 km, the time taken for the round trip is
t = (1 km)/(V+1 km/h) + (1 km)/(v-1 km/h)
= (V-1 + V+1)/(V² - 1)
= (2V)/(V² - 1)
The time for the round trip is 50 min = 5/6 h.
Therefore
(2V)/(V² - 1) = 5/6
5(V² - 1) = 12V
5V² - 12V - 5 = 0
Solve with the quadratic formula.
V = (1/10)*[12 +/- √(144 + 100)] = 2.762 or -0.362 km/h
Ignore negative speed, so that
V = 2.762 k/h
Answer:
The speed of the boat relative to the water is
2.76 km/h (nearest hundredth)
Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
This is mathematically represented as
<u>F= (G X m1 x m2) /r∧2</u>
where F is the force acting between the charged particles
r is the distance between the two charges measured in m
G is the gravitational constant which has a value of <em>6.674×10^-11 Nm^2 kg^-2</em>
m1 and m2 are the masses of the objects measured in Kg
Now if the distance between the is doubled then r becomes 2r. Substituting this in the above formula we get the new Force as
Force (new) = (G X m1 x m2) /(2r)∧2
Thus dividing Force(new)/Force we get
Force(new)/Force = 1/4.
Thus the gravitational force becomes 1/4th of the original value if the distance between the two masses are doubled.
Answer:
λ= 2455 nm
Explanation:
Constructive interference occurs when the optical path difference is equal to an integer multiple of wavelength. Let's examine the reflection on each face
On the first surface we go from a lower medium refractive index (air) to one with a higher index (film), whereby a phase change of pi (180º) is introduced. On the second surface instead of the beginning of refraction, it is from a higher index to a smaller one, so there is no phase change, with this we can write the normal interference equation.
2 t = (m + ½)
The term lann is the wavelength in the film that is related to the wavelength in the air by
= λ / n
2t = (m + ½) λ / n
λ = 2t n / (m + ½)
For the first constructive interference m = 0
λ = 2 0.448 10⁻⁶ 1.37 / (0 + ½)
λ = 2,455 10⁻⁶ m
λ = 2,455 10⁻⁶ m (10⁹ nm / 1m)
λ= 2455 nm
For m = 1
λ = 2 0.448 10-6 1.37/ (1 + ½)
λ = 0.81835 10-6 m
λ = 818 nm
We can observe that the length and where it corresponds to ultraviolet light, so there is no constructive interference for visible light.