Option(a) the mass of cart 2 is twice that of the mass of cart 1 is the right answer.
The mass of cart 2 is twice that of the mass of cart 1 is correct about the mass of cart 2.
Let's demonstrate the issue using variables:
Let,
m1=mass of cart 1
m2=mass of cart 2
v1 = velocity of cart 1 before collision
v2 = velocity of cart 2 before collision
v' = velocity of the carts after collision
Using the conservation of momentum for perfectly inelastic collisions:
m1v1 + m2v2 = (m1 + m2)v'
v2 = 0 because it is stationary
v' = 1/3*v1
m1v1 = (m1+m2)(1/3)(v1)
m1 = 1/3*m1 + 1/3*m2
1/3*m2 = m1 - 1/3*m1
1/3*m2 = 2/3*m1
m2 = 2m1
From this we can conclude that the mass of cart 2 is twice that of the mass of cart 1.
To learn more about inelastic collision visit:
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The statement 'both allow citizens to vote for members of the legislature' describes a similarity between presidential and parliamentary democracies. They are different forms of government.
<h3>Presidential and parliamentary democracies</h3>
Democracy refers to a form of government where people vote to choose authorities designed to decide legislation.
A presidential democracy is when the presented is voted to be the head of government (president) separately from the legislative system.
Parliamentary democracy is a form of government where the political party having the greatest representation in the legislature forms the government.
Learn more about presidential and parliamentary democracies here:
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Answer:
v₀ₓ = 63.5 m/s
v₀y = 54.2 m/s
Explanation:
First we find the net launch velocity of projectile. For that purpose, we use the formula of kinetic energy:
K.E = (0.5)(mv₀²)
where,
K.E = initial kinetic energy of projectile = 1430 J
m = mass of projectile = 0.41 kg
v₀ = launch velocity of projectile = ?
Therefore,
1430 J = (0.5)(0.41)v₀²
v₀ = √(6975.6 m²/s²)
v₀ = 83.5 m/s
Now, we find the launching angle, by using formula for maximum height of projectile:
h = v₀² Sin²θ/2g
where,
h = height of projectile = 150 m
g = 9.8 m/s²
θ = launch angle
Therefore,
150 m = (83.5 m/s)²Sin²θ/(2)(9.8 m/s²)
Sin θ = √(0.4216)
θ = Sin⁻¹ (0.6493)
θ = 40.5°
Now, we find the components of launch velocity:
x- component = v₀ₓ = v₀Cosθ = (83.5 m/s) Cos(40.5°)
<u>v₀ₓ = 63.5 m/s</u>
y- component = v₀y = v₀Sinθ = (83.5 m/s) Sin(40.5°)
<u>v₀y = 54.2 m/s</u>
Answer:
Explanation:
The problem is based on the concept of Doppler's effect of em wave .
Expression for apparent frequency can be given as follows
n = N x (V - v ) / ( V + v )
n is apparent frequency , N is real frequency , V is velocity of light and v is velocity of cloud.
n = 6 x 10⁹ ( 3 x 10⁸ - 8.52 ) / ( 3 x 10⁸ + 8.52 )
= 6 x 10⁹ ( 3 x 10⁸ ) ( 3 x 10⁸ + 8.52 )⁻¹
= 6 x 10⁹ ( 3 x 10⁸ ) ( 3 x 10⁸)⁻¹ ( 1 + 8.52/3 x 10⁸ )⁻¹
= 6 x 10⁹ ( 1 - 8.52/3 x 10⁸ )
= 6 x 10⁹ - 6 x 10⁹x 8.52/ (3 x 10⁸ )
= 6 x 10⁹ 1 - 170 .
So change in frequency = 170 approx.
<h3><u>Answer;</u></h3>
= 4.19 Joules
<h3><u>Solution;</u></h3>
Energy stored in capacitor = U = 8.38 J
U =(1/2)CV^2
C =(eo)A/d
C*d=(eo)A=constant
C2d2=C1d1
C2=C1d1/d2
Initial separation between the plates =d1= 2.30mm .
Final separation = d2 = 1.15 mm
But; Energy=U =(1/2)q^2/C
U2C2 = U1C1
U2 =U1C1 /C2
U2 =U1d2/d1
Final energy = Uf = initial energy × d2/d1
= 8.38 ×1.15/2.30
= 4.19 Joules
Thus; The final energy = 4.19 Joules
