<span>a. The magnitude of the vector is doubled as well.
Let's say we have a 2-dimensional vector with components x and y.
It's magnitude lâ‚ is given by:
lâ‚ = âš(x² + y²)
If we double the components x and y, the new magnitude lâ‚‚ is:
lâ‚‚ = âš((2x)² + (2y²))
With a bit of algebra...
lâ‚‚ = âš(4x² + 4y²)
lâ‚‚ = âš4(x² + y²)
lâ‚‚ = 2âš(x² + y²)
We can write the new magnitude lâ‚‚ in terms of the old magnitude lâ‚.
lâ‚‚ = 2lâ‚
Therefore, the new magnitude is double the old one.
It should be clear that this relationship applies to 3D (and 1D) vectors as well.
b. The direction angle is unchanged.
The direction angle θ₠for a 2-dimensional vector is given by:
θ₠= arctan(y / x)
If we double both components, we get:
θ₂ = arctan(2y / 2x)
θ₂ = arctan(y / x)
θ₂ = θâ‚
The new direction angle is the same as the old one.</span>
Answer:
Explanation:
Given
--- Surface Tension
--- Radius
Required
Determine the required force
First, we calculate the circumference (C) of the circular plate
The applied force is then calculated using;
Answer:
Explanation:
First of all, we need to find the pressure exerted on the sphere, which is given by:
where
is the atmospheric pressure
is the water density
is the gravitational acceleration
is the depth
Substituting,
The radius of the sphere is r = d/2= 1.1 m/2= 0.55 m
So the total area of the sphere is
And so, the inward force exerted on it is
Answer:
the max is 2,500 or less
Explanation:
because you cant owe anymore