Answer:
We are given the trajectory of a projectile:
y=H+xtan(θ)−g2u2x2(1+tan2(θ)),
where H is the initial height, g is the (positive) gravitational constant and u is the initial speed. Since we are looking for the maximum range we set y=0 (i.e. the projectile is on the ground). If we let L=u2/g, then
H+xtan(θ)−12Lx2(1+tan2(θ))=0
Differentiate both sides with respect to θ.
dxdθtan(θ)+xsec2(θ)−[1Lxdxdθ(1+tan2(θ))+12Lx2(2tan(θ)sec2(θ))]=0
Solving for dxdθ yields
dxdθ=xsec2(θ)[xLtan(θ)−1]tan(θ)−xL(1+tan2(θ))
This derivative is 0 when tan(θ)=Lx and hence this corresponds to a critical number θ for the range of the projectile. We should now show that the x value it corresponds to is a maximum, but I'll just assume that's the case. It pretty obvious in the setting of the problem. Finally, we replace tan(θ) with Lx in the second equation from the top and solve for x.
H+L−12Lx2−L2=0.
This leads immediately to x=L2+2LH−−−−−−−−√. The angle θ can now be found easily.
Answer:
7.46×10⁻⁶ m
Explanation:
Applying,
F = kqq'/r²............ Equation 1
make r the subject of the equation
r = √(F/kqq').......... Equation 2
From the question,
Given: F = 8 N, q' = q= 4 C
Constant: k = 8.98×10⁹ Nm²/C²
Substitute these values into equation 2
r = √[8/(4×4×8.98×10⁹)]
r = √(55.7×10⁻¹²)
r = 7.46×10⁻⁶ m
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An advertising method in which the buyers are persuaded to buy a product by deliberately disguising information and trying to distort actual details by suppressing the holistic information on the product.
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Learn more: brainly.com/question/3163475
Wow ! This question reads like it might have come from one of
Faraday or Maxwell's original laboratory notebooks.
Choice-A is the correct one, when you consider what "conductance"
means. Conductance is just 1/resistance .
So when you see
"A) Current is proportionate to the conductance of the circuit and
precisely proportional to the voltage applied across the circuit."
what it's saying is
"Current is inversely proportional to the resistance of the circuit, and
directly proportional to the voltage applied across the circuit."
If you write the equation for all those words, it looks like
I = V / R
and that's correct.
Assuming that the densities of the gases are:
density of air, ρ1 = 1.29 kg / m^3
density of helium, ρ2 = 0.179 kg / m^3
Since buoyant force and weight are two forces that are in
opposite direction (buoyant force is up while weight is down), therefore equate
the two:
buoyant force = weight
m g = (800 + m1) g
where m is the mass of buoyancy, g is gravity and m1 is
the maximum mass of the cargo
m = 800 + m1
We know that mass is also expressed as:
m = ρ V
where ρ is density of gas and V is volume of the sphere
Since there are two interacting gases here, therefore m
is:
m = (ρ1 – ρ2) V
Therefore:
(ρ1 – ρ2) V = 800 + m1
(1.29 – 0.179) (4π/3) (8.35m)^3 = 800 + m1
2709.33 = 800 + m1
m1 = 1,909.33 kg
