First
let us imagine the projectile launched at initial velocity V and at angle
θ relative to the horizontal. (ignore wind resistance)
Vertical component y:
The
initial vertical velocity is given as Vsinθ
The moment the projectile reaches the maximum
height of h, the vertical velocity
will be 0, therefore the time t taken to attain this maximum height is:
h = Vsinθ - gt
0 = Vsinθ - gt
t = (Vsinθ)/g
where
g is acceleration due to gravity
Horizontal component x:
The initial horizontal velocity is given as Vcosθ. However unlike
the vertical component, this horizontal velocity remains constant because this is unaffected by gravity. The time to travel the
horizontal distance D is twice the value of t times the horizontal velocity.
D = Vcosθ*[(2Vsinθ)/g]
D = (2V²sinθ cosθ)/g
D = (V²sin2θ)/g
In order for D (horizontal distance) to be
maximum, dD/dθ = 0
That is,
2V^2 cos2θ / g = 0
And since 2V^2/g must not be equal to zero, therefore cos(2θ) = 0
This is true when 2θ = π/2 or θ = π/4
Therefore it is now<span> shown that the maximum horizontal travelled is attained when
the launch angle is π/4 radians, or 45°.</span>
Answer : The final pressure of the system in atm is, 3.64 atm
Explanation :
Boyle's Law : It is defined as the pressure of the gas is inversely proportional to the volume of the gas at constant temperature and number of moles.
or,
where,
= first pressure = 8.19 atm
= second pressure = 2.65 atm
= first volume = 2.14 L
= second volume = 9.84 L
= final pressure = ?
= final volume = 2.14 L + 9.84 L = 11.98 L
Now put all the given values in the above equation, we get:
Therefore, the final pressure of the system in atm is, 3.64 atm
Reflection: a change in direction of a wave at a boundary between two different media.
sentence: i saw my reflection in the mirror.
refraction: the bending of light as it passes from one transparent substance into another.
sentence: when light goes through glass, it’s a refraction.
diffraction: the bending of waves around the corners of an obstacle.
sentence: spaced tracks on a CD act as a diffraction.
absorption: the process or action by which one thing absorbs or is absorbed by another.
sentence: heat waves hitting the beach usually give most of their energy to the sand.
interference: when two waves lay on each other and their energies are either added together or cancelled out.
sentence: interference waves can be observed with all types of waves.
standing wave: two waves moving in opposite directions. they both have the same amplitude or frequency.
sentence: plucking the string of a guitar is an example of standing waves.
resonance: increased amplitude that occurs when the frequency of a force is equal or close to a natural frequency.
sentence:a buzz in your car that only occurs at a certain speed is an example or resonance.
