Explanation:
(a)
The initial vertical velocity is 13 m/s. At the maximum height, the vertical velocity is 0 m/s.
v = at + v₀
0 = (-9.8) t + 13
t ≈ 1.33 s
(b)
Immediately prior to the explosion, the ball is at the maximum height. Here, the vertical velocity is 0 m/s, and the horizontal velocity is constant at 25 m/s.
v = √(vx² + vy²)
v = √(25² + 0²)
v = 25 m/s
(c)
Momentum is conserved before and after the explosion.
In the x direction:
m vx = ma vax + mb vbx
m (25) = (⅓ m) (0) + (⅔ m) (vbx)
25m = (⅔ m) (vbx)
25 = ⅔ vbx
vbx = 37.5 m/s
And in the y direction:
m vy = ma vay + mb vby
m (0) = (⅓ m) (0) + (⅔ m) (vby)
0 = (⅔ m) (vby)
vby = 0 m/s
Since the vertical velocity hasn't changed, and since Fragment B lands at the same height it was launched from, it will have a vertical velocity equal in magnitude and opposite in direction as its initial velocity.
vy = -13 m/s
And the horizontal velocity will stay constant.
vx = 37.5 m/s
The velocity vector is (37.5 i - 13 j) m/s. The magnitude is:
v = √(vx² + vy²)
v = √(37.5² + (-13)²)
v ≈ 39.7 m/s
Answer with Explanation:
Let rest mass 
at point P at distance x from center of the planet, along a line connecting the centers of planet and the moon.
Mass of moon=m
Distance between the center of moon and center of planet=D
Mass of planet=M
We are given that net force on an object will be zero
a.We have to derive an expression for x in terms of m, M and D.
We know that gravitational force=
Distance of P from moon=D-x
=Force applied on rest mass due to m
=Force on rest mass due to mas M
because net force is equal to 0.
Let 
Then, 
b.We have to find the ratio R of the mass of the mass of the planet to the mass of the moon when x=
Net force is zero
Hence, the ratio R of the mass of the planet to the mass of the moon=4:1
Answer:
The frequency does not depend on the amplitude for any (ideal) mechanical or electromagnetic waves.
In electromagnetism we have that the relation is:
Velocity = wavelenght*frequency.
So the amplitude of the wave does not have any effect here.
For a mechanical system like an harmonic oscillator (that can be used to describe almost any oscillating system), we have that the frequency is:
f = (1/2*pi)*√(k/m)
Where m is the mass and k is the constant of the spring, again, you can see that the frequency only depends on the physical properties of the system, and no in how much you displace it from the equilibrium position.
This happens because as more you displace the mass from the equilibrium position, more will be the force acting on the mass, so while the "path" that the mass has to travel is bigger, the mas moves faster, so the frequency remains unaffected.
Light travels in a straight line because it doesn't usually interact with its medium. When it does it is called refraction.
