Amodel rocket is fired vertically upward from rest. its acceleration for the first three seconds is a(t) = 96t, at which time the fuel is exhausted and it becomes a freely "falling" body. nineteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to −16 ft/s in 5 s. the rocket then "floats" to the ground at that rate.

a) determine the position function s and the velocity function v (for all times t).
b) at what time does the rocket reach its maximum height?

what is that height? (round your answer to the nearest integer.)

c) at what time does the rocket land? (round your answer to one decimal place.)

In kinematics questions we need to separate the question into different parts if the acceleration changes. Here, there are three time intervals where acceleration is different.

1) a(t) = 96t. We can find the velocity function of the rocket by integrating the acceleration function. Then we can integrate again to find the position function.

'C' is the integration constant. We can find this constant by investigating the initial conditions.

We know that the rocket is initially at rest, so 'C' should be zero.

Again, the rocket started from ground zero, so C = 0.

We should conclude the first part by calculating the final position and final velocity of the rocket.

2) For the second part, the rocket is in free fall, so

The maximum height that the rocket reaches is when its velocity is zero.

So,

The maximum height is

The final positions for the part 2 is

3) With the parachute, the velocity is dropped from -276.4 to 16 in 5 s.

The rocket lands

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:

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:

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

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.