The question is unclear regarding the boat's velocity. Is it 20 m/s south relative to the water, or relative to the earth? (It is a river, after all...)
There's also the possibility that the boat's velocity relative to the river is 0. Take the south direction to be negative and north to be positive, and denote by the velocity of a body A relative to a body B. Under these conditions,
(B for boat, E for earth, W for water) so that the passenger's velocity relative to the earth is
(P for passenger)
or 10 m/s south.
The y-component of the initial velocity vector is zero only in scenarios A and C. The weight/package on either plane inherits a non-zero x-component that matches the plane's horizontal velocity, but with respect to the vertical direction the objects are at rest, and dropping them from a given height doesn't confer them an initial vertical velocity. On the other hand, if the object was thrown upward and allowed to fall, or shot downward by a cannon, then the initial vertical velocity would be non-zero.
In scenario B, the dolphin must have some non-zero y-component of velocity in order to launch itself out of the water, because otherwise it would stay at a fixed depth.
The relationship between object distance, image distance, and focal length of a spherical mirror is given by
1/f=1/v+1/u
Where
f= focal length of a spherical mirror (distance between the pole and the principal focus of the mirror)
u= object distance (distance between pole and object)
v= image distance (the distance between pole and image)
Answer:
According to Einstein's famous equation, matter can convert into energy (and viceversa) as follows:
where
E is the energy
m is the mass
c is the speed of light ()
Given the huge value of , we see that even a tiny amount of matter is able to release a huge amount of energy, when the whole mass is converted into energy. This is precisely what happens in nuclear reactions. For example, in the process of nuclear fusion (that occurs in the core of the stars), two light nuclei fuse together into a heavier nucleus. The mass of the final nucleus is lower than the total mass of the initial nuclei, so part of the mass has been converted into energy according to the equation above: this is why the amount of energy produced by stars is so big.