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.
They do not react with or chemically bond to each other.
Answer: Curved mirrors often reflect a distorted image that looks different from how you look in real life. Low-quality mirrors are also likely to produce image distortions and give your face an asymmetrical appearance, which is perceived as ugly.
Explanation:
Answer:
Inducted Magnetic field will be toward from you
Inducted current direction will be counter clockwise.
Explanation:
Lenz's law states that the direction of the current induced in a wire by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.
So if the field begins to decrease, the induced magnetic field would try to stop this, so its direction will be the same as the magnetic field, toward from you.
This induced magnetic field is produced by the current in the wire. If the inducted magnetic field will be toward you, the right hand rule says that the direction from the inducted current will be counter clockwise.
The total work is
(mass of the elevator, kg) x (9.8 m/s²) x (9.0 m) Joules .