<span>The ball with an initial velocity of 2 m/s rebounds at 3.6 m/s
The ball with an initial velocity of 3.6 m/s rebounds at 2 m/s
There are two principles involved here
Conservation of momentum and conservation of energy.
I'll use the following variables
a0, a1 = velocity of ball a (before and after collision)
b0, b1 = velocity of ball b (before and after collision)
m = mass of each ball.
For conservation of momentum, we can create this equation:
m*a0 + m*b0 = m*a1 + m*b1
divide both sides by m and we get:
a0 + b0 = a1 + b1
For conservation of energy, we can create this equation:
0.5m(a0)^2 + 0.5m(b0)^2 = 0.5m(a1)^2 + 0.5m(b1)^2
Once again, divide both sides by 0.5m to simplify
a0^2 + b0^2 = a1^2 + b1^2
Now let's get rid of a0 and b0 by assigned their initial values. a0 will be 2, and b0 will be -3.6 since it's moving in the opposite direction.
a0 + b0 = a1 + b1
2 - 3.6 = a1 + b1
-1.6 = a1 + b1
a1 + b1 = -1.6
a0^2 + b0^2 = a1^2 + b1^2
2^2 + -3.6^2 = a1^2 + b1^2
4 + 12.96 = a1^2 + b1^2
16.96 = a1^2 + b1^2
a1^2 + b1^2 = 16.96
The equation a1^2 + b1^2 = 16.96 describes a circle centered at the origin with a radius of sqrt(16.96). The equation a1 + b1 = -1.6 describes a line with slope -1 that intersects the circle at two points. Those points being (a1,b1) = (-3.6, 2) or (2, -3.6). This is not a surprise given the conservation of energy and momentum. We can't use the solution of (2, -3.6) since those were the initial values and that would imply the 2 billiard balls passing through each other which is physically impossible. So the correct solution is (-3.6, 2) which indicates that the ball going 2 m/s initially rebounds in the opposite direction at 3.6 m/s and the ball originally going 3.6 m/s rebounds in the opposite direction at 2 m/s.</span>
What property/properties of water allowed the water to stick to the penny?
Solution's:
Explanation:
By these properties, the water molecules gets attracted to the other molecules. Hence, this makes the water get stick to the penny.
Answer:
1.152 miles
Explanation:
Given: central angle = 1 minute = 
radius of the earth = 3960 miles
The length of an arc = 
2
r
where: 
is the central angle, and r is the radius.
Thus,
Distance along the arc = 2r
Distance along the arc = 
x 2 x 
x 3960
= x 24891.4286
= 1.1524
The required distance along an arc is 1.152 miles.
Answer:
Explanation:
Let the speed of light in vacuum is c and the speed of light in medium is v. Let the angle of incidence is i.
By using the definition of refractive index
refractive index of the medium is given by
n = speed of light in vacuum / speed of light in medium
n = c / v ..... (1)
Use Snell's law
n = Sin i / Sin r
Where, r be the angle of refraction
From equation (1)
c / v = Sin i / Sin r
Sin r = v Sin i / c
The x-component of this vector inclined from the horizontal axis is 15m.
<h3>What is vector?</h3>
A vector is the representation of a physical quantity in magnitude and direction.
A vector incline at an angle in has two components. On in x direction and other is in y direction.
For the given length of vector = 45.6 m and the angle of inclination from the +x axis θ = 70.8°
The x component of the given vector is
= 45.6cos 70.8°
= 14.99 m
Thus, the x- component of this vector is 15m.
Learn more about vector.
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