Acelebrating student throws a water balloon horizontally from a dormitory window that is 50 m above the ground. it hits the ground at a point 60 m from the building without appreciable air resistance.(a) what will be the horizontal component of the velocity of the balloon just before it hits the ground? (b) what will be the magnitude of the vertical velocity of the balloon just before it hits the ground?

a) The horizontal velocity of the balloon just before it hits the ground is 6 m/s

b) The magnitude of the vertical velocity of the balloon just before it hits the ground is 98 m/s.

Explanation:

Hi there!

The velocity and position vectors of the water balloon are given by the following equations:

r =(x0 + v0x · t, y0 + v0y · t + 1/2 · g · t²)

v =(v0x, v0y + g · t)

where:

r = position vector at time t.

x0 = initial horizontal position.

v0x = initial horizontal velocity.

t = time.

y0 = initial vertical position.

v0y = initial vertical position.

g = acceleration due to gravity (-9.8 m/s² considering the upward position as positive) .

v = velocity vector at time t.

a) Please, see the attached figure for a graphic description of the problem.

Considering the origin of the frame of reference as the point of launch, notice that the position vector when the balloon hits the ground is

r1 = (60, -50) m

Then:

r1x = 60 m = v0x · t

r1y = -50 m = 1/2 · (-9.8 m/s²) · t²

(notice that the initial vertical velocity is zero, see figure).

Solving r1y for t:

(-50 m · 2) / -9.8 m/s² = t²

t = 10 s

Now, let´s replace t in the r1x equation and solve it for the horizontal component of the velocity:

60 m = v0x · 10 s

v0x = 60 m / 10 s

v0x = 6 m/s

The initial horizontal component of the velocity is 6 m/s. This velocity is constant because there is no air resistance. Then, just before the balloon hits the ground, it will have a horizontal velocity of 6 m/s.

b) To calculate the vertical component of the velocity when the balloon hits the ground, let´s use the equation of the vertical component of the velocity:

v1y = v0y + g · t

Since v0y = 0

v1y = -9.8 m/s² · (10 s) = -98 m/s

The magnitude of the vertical velocity of the balloon when it hits the ground is 98 m/s.

quantum mechanics or quantum physics is physics of very small objects (particles) and physical entities.

quantum physics has some parallels to our macro world and some pretty unique ideas which theoretically and mathematically proven to be true even though we will never be able to access them because of our size.

there are many types of particles: subatomic, elementary etc.

subatomic means they are smaller than atom, elementary means they are at the very basis of everything.

subatomic particles are for eg. protons, neutrons but not electrons.

elementary particles are categorised into 3 groups by what they do.

these 3 groups are quarks, leptons and bosons.

light for example is a particle more precisely a photon a part of leptons.

proton (subatomic particle) is made out of 2 up quarks and 1 down quark each of these has a fractional charge like . (i crazy)

most famous scientist who contributed to this physics are:

max planckalbert einsteinerwin schrödingermany

the topic itself us understand a lot and will probably be vastly used in the future (quantum computers, understanding the big bang,

we also must not forget quantum effects like:

superposition (where 1 thing can be this and that at the same time),entanglement (where two particles are seemingly connected by some sort of unknown (or known) force, energy, matter (i know all that can be the same at least it was at the beginning)

and there is more. but probably too much for this answer to be consistent due to my average understanding of this topic.

hope this you understand quantum mechanics a little more. i'm not an expert in the topic (so don't be like wth if you are an expert) but i'm very interested in it.

anyways quantum physics is a very hard topic (harder than physics (perhaps)) therefore searching for every information there is about it and learning it is unfortunately impossible (you can only specialise into 1 - 3 things or more (perhaps

have fun and i wish you luck!

r3t40

The answer is frictional force