Answer:
h = 16.9 m
Explanation:
When a ball is thrown upward, its velocity gradually decreases, until it stops for a moment, when it reaches the maximum height, while its height increases. Thus, the law conservation of energy states in this case, that:
Kinetic Energy Lost by Ball = Potential Energy Gained by Ball
(0.5)m(Vf² - Vi²) = mgh
h = (0.5)(Vf² - Vi²)/g
where,
Vf = Final Speed of Ball = 0 m/s (Since, ball stops for a moment at highest point)
Vi = Initial Speed of Ball = 18.2 m/s
g = acceleration due to gravity = - 9.8 m/s² ( negative for upward motion)
h = maximum height the ball can reach = ?
Therefore, using values in the equation, we get:
h = (0.5)[(0 m/s)² - (18.2 m/s)²]/(-9.8 m/s²)
<u>h = 16.9 m</u>
Momentum- most commonly used in physics and STEM, is the quantity of motion of a moving body, measured as a product of its mass and velocity.
Answer:
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Explanation:
Given data
mass = 3 slugs = 3 * 32.14 = 96.52 lbs
constant k = 9 lbs/ft
Beta = 6lbs * s/ft
mass is pulled = 1 ft below
to find out
equation of motion for the mass
solution
we know that The mass is pulled 1 ft below so
we will apply here differential equation of free motion i.e
dx²/dt² + 2 α dx/dt + ω² x =0 ........................1
here 2 α = Beta / mass
so 2 α = 6 / 96.52
α = 0.031
α² = 0.000961 ...............2
and
ω² = k/mass
ω² = 9 /96.52
ω² = 0.093 ..................3
we can say that from equation 2 and 3 that α² - ω² = -0.092239
this is less than zero
so differential equation is
x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
The average kinetic energy of the gas would also be constant since the temperature of the gas is not changing.
<h3>What happens to the average kinetic energy?</h3>
The kinetic energy is the energy of the particle that is motion. We know that the kinetic energy of the gas is proportional to the temperature of the gas. As the temperature increases, the kinetic energy of the particles of the gas increases.
Now we can see that the gas has been maintained at a constant temperature and a constant volume and that the particles of the gas collide with each other. This implies that the average kinetic energy of the gas would also be constant since the temperature of the gas is not changing.
Learn more about average kinetic energy:brainly.com/question/1599923
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Answer:


Explanation:
m = Mass of proton = 
v = Speed of proton = 0.5c = 
Circumference of the colider is 7 km


Centripetal acceleration is 

Force on protons is 