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:
Explanation:
The statement is described physically by means of the Principle of Momentum Conservation. Let assume that first person moves in the positive direction:
First Person
Second Person
The final velocities of the two people after the snowball is exchanged is:
Explanation:
The shorter wavelength electromagnetic waves from sun are absorbed by earth material in form of short wavelength and the radiated wavelength are longer ones. Also higher energy waves are of shorter wavelength and lower energy waves have longer wavelength. So, they are absorbed as short wavelength and radiated back as long wavelength.
C) Acceleration is the rate of change of velocity of an object. Velocity is the speed and direction of an object so acceleration is used to describe the rate of change. I hope this helps!!
