Answer:
a)
Y0 = 0 m
Vy0 = 15 m/s
ay = -9.81 m/s^2
b) 7.71 m
c) 3.06 s
Explanation:
The knowns are that the initial vertical speed (at t = 0 s) is 15 m/s upwards. Also at that time the dolphin is coming out of the water, so its initial position is 0 m. And since we can safely assume this happens in Earth, the acceleration is the acceleration of gravity, which is 9.81 m/s^2 pointing downwards
Y(0) = 0 m
Vy(0) = 15 m/s
ay = -9.81 m/s^2 (negative because it points down)
Since acceleration is constant we can use the equation for uniformly accelerated movement:
Y(t) = Y0 + Vy0 * t + 1/2 * a * t^2
To find the highest point we do the first time derivative (this is the speed:
V(t) = Vy0 + a * t
We equate this to zero
0 = Vy0 + a * t
0 = 15 - 9.81 * t
15 = 9.81 * t
t = 0.654 s
At this time it will have a height of:
Y(0.654) = 0 + 15 * 0.654 - 1/2 * 9.81 * 0.654^2 = 7.71 m
The doplhin jumps and falls back into the water, when it falls again it position will be 0 again. So we can equate the position to zero to find how long it was in the air knowing that it started the jump at t = 0s.
0 = Y0 + Vy0 * t + 1/2 * a * t^2
0 = 0 + 15 * t - 1/2 * 9.81 t^2
0 = 15 * t - 4.9 * t^2
0 = t * (15 - 4.9 * t)
t1 = 0 This is the moment it jumped into the air
0 = 15 - 4.9 * t2
15 = 4.9 * t2
t2 = 3.06 s This is the moment when it falls again.
3.06 - 0 = 3.06 s
The best use of an atomic model to explain the charge of the particles in Thomson's beams is:
<u>An atom's smaller negative particles are at a distance from the central positive particles, so the negative particles are easier to remove.</u>
<u>Explanation:</u>
In Thomson's model, an atom comprises of electrons that are surrounded by a group of positive particles to equal the electron's negative particles, like negatively charged “plums” that are surrounded by positively charged “pudding”.
Atoms are composed of a nucleus that consists of protons and neutrons . Electron was discovered by Sir J.J.Thomson. Atoms are neutral overall, therefore in Thomson’s ‘plum pudding model’:
-
atoms are spheres of positive charge
- electrons are dotted around inside
Thomson's conclusions made him to propose the Rutherford model of the atom where the atom had a concentrated nucleus of positive charge and also large mass.
Water gets to the leaves in the tops of the tallest trees by something called the cohesion-tension theory. Water has two very unique properties called adhesion and cohesion. Cohesion is the tendency of water molecules to stick together with one another. The water sticks together, leaving no room for air, strengthening the "force" of the water going up the tree. The water also sticks to the sides of the xylem inside the tree. In addition to these properties, there are also the factors of negative and positive water potential. For more information, look up more details of the cohesion-tension theory.
Answer:
a
The orbital speed is 
b
The escape velocity of the rocket is 
Explanation:
Generally angular velocity is mathematically represented as
Where T is the period which is given as 1.6 days = 
Substituting the value
At the point when the rocket is on a circular orbit
The gravitational force = centripetal force and this can be mathematically represented as
Where G is the universal gravitational constant with a value 
M is the mass of the earth with a constant value of 
r is the distance between earth and circular orbit where the rocke is found
Making r the subject
![r = \sqrt[3]{\frac{GM}{w^2} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BGM%7D%7Bw%5E2%7D%20%7D)
![= \sqrt[3]{\frac{6.67*10^{-11} * 5.98*10^{24}}{(4.45*10^{-5})^2} }](https://tex.z-dn.net/?f=%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B6.67%2A10%5E%7B-11%7D%20%2A%205.98%2A10%5E%7B24%7D%7D%7B%284.45%2A10%5E%7B-5%7D%29%5E2%7D%20%7D)
The orbital speed is represented mathematically as
Substituting value
The escape velocity is mathematically represented as
Substituting values
