The plane's velocity of 35.11 m/s is actually due in a north-eastward direction. The 12 m/s velocity is the vertical component of the plane's velocity, hence it is pointing northwards. We will use the formula:
Vy = Vsin∅
To determine the angle ∅ at which the plane is flying. This is:
12 = 35.11 * sin∅
∅ = 20.0 degrees
The eastward velocity is:
Vx = Vcos∅
Vx = 35.11 * cos(20)
Vx = 33.0 m/s
The plane's eastward velocity is 33.0 m/s
Answer:
$ 3085713685.71
Explanation:
= Actual wavelength = 700 nm
= Changed wavelength = 500 nm
Let the wavelength of red color be 700 nm and green be 500 nm
Change in wavelength is
We have the relation
The speed of the vehicle is 85714285.7143 m/s
By how much was the car speeding
The number of 10 km/h in the above speed
Cost of the ticket
The cost of the ticket is $ 3085713685.71
All of that fluff at the beginning is interesting, but completely irrelevant
to the question. The question is just asking for the mass of an object
that weighs 3.6N on Earth.
Weight = (mass) x (acceleration of gravity)
3.6N = (mass) x (9.8 m/s²)
Divide each side
by 9.8 m/s : Mass = 3.6N / 9.8 m/s² = <em>0.367 kilogram</em> (rounded)
Write each force in component form:
<em>v </em>₁ : 50 N due east → (50 N) <em>i</em>
<em>v</em> ₂ : 80 N at N 45° E → (80 N) (cos(45°) <em>i</em> + sin(45°) <em>j</em> ) ≈ (56.5 N) (<em>i</em> + <em>j</em> )
The resultant force is the sum of these two vectors:
<em>r</em> = <em>v </em>₁ + <em>v</em> ₂ ≈ (106.5 N) <em>i</em> + (56.5 N) <em>j</em>
Its magnitude is
|| <em>r</em> || = √[(106.5 N)² + (56.5 N)²] ≈ 121 N
and has direction <em>θ</em> such that
tan(<em>θ</em>) = (56.5 N) / (106.5 N) → <em>θ</em> ≈ 28.0°
i.e. a direction of about E 28.0° N. (Just to clear up any confusion, I mean 28.0° north of east, or 28.0° relative to the positive <em>x</em>-axis.)
