15) A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. If the ground at the base of the cliff is level, which rock hits the ground with the greatest speed if there is no air resistance?
A) Rock X
B) Rock Y
C) Rock Z
D) They all hit the ground with the same speed.
Why is the answer D?

All three rocks start at the same height, so they have the same potential energy. They also start with the same speed (even though they're in different directions), so they have the same kinetic energy.

Energy is conserved, so when they land, all the potential energy is converted into kinetic energy. Therefore, they must all have the same speed (though not necessarily the same direction).

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Cricetus Cricetus · Answer 2 · 2021-10-22T06:47:51+02:00

They all hit the ground with the same speed. A further explanation is below.

Let,

Each rock,

(X, Y, and Z)

Mass,

m

Initial speed,

u

Whenever rock X returns from its top altitude to the cliff's elevation, the latter's speed would be "u." As a result, plenty of the stones traveled the very same distances from either the mountain towards the surface simultaneously beginning speed such as under acceleration ([tex]g = 9.8 \ m/s^2[/tex]).

i.e., they all're having the same final speed "v". Given by:

[tex]v^2=u^2+2gh[/tex]

hence,

Just before hitting the ground, they all will have the same Kinetic energy.

[tex]K.E = \frac{1}{2}mv^2[/tex]

Thus the above response i.e., option D) is the right answer.

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