The velocity of the red cart after the collision is 2 m/s
From the law of conservation of momentum, initial momentum of system = final momentum of system.
m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄ where m₁ = mass of red cart = 4 kg, v₁ = velocity of red cart before collision = + 4 m/s, v₃ = velocity of red cart after collision, m₂ = mass of blue cart = 1 kg, v₂ = velocity of blue cart before collision = 0 m/s (since it is initially at rest) and v₄ = velocity of blue cart after collision = + 8 m/s.
Substituting the values of the variables into the equation, we have,
m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄
4 kg × 4 m/s + 1 kg × 0 m/s = 4v₃ + 1 kg × 8 m/s
16 kgm/s + 0 kgm/s = 4v₃ + 8 kgm/s
16 kgm/s = 4v₃ + 8 kgm/s
16 kgm/s - 8 kgm/s = (4 kg)v₃
(4 kg)v₃ = 8 kgm/s
Divide both sides by 4 kg, we have
v₃ = 8 kgm/s ÷ 4 kg
v₃ = 2 m/s
The velocity of the red cart after the collision is 2 m/s.
Learn more about conservation of momentum here:
brainly.com/question/7538238
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If west means the west of the axis x the velocity equal :
Answer:
8.6 m/s
Explanation:
The observer is stationary
The source is moving
Let v₀ be the speed of sound in the air
Let v be the speed of the ambulance
As the siren approaches
f₁ = 2000(v₀ / (v₀ - v))
As the siren departs
f₁' = 2000(v₀ / (v₀ + v))
f₁ - f₁' = 100
2000(v₀ / (v₀ - v)) - 2000(v₀ / (v₀ + v)) = 100
v₀ / (v₀ - v) - v₀ / (v₀ + v) = 100/2000
v₀(v₀ + v) / (v₀ - v)(v₀ + v) - v₀(v₀ - v) / (v₀ - v)(v₀ + v) = 0.05
(v₀² + vv₀) - (v₀² - vv₀) / (v₀² - v²) = 0.05
2vv₀ / (v₀² - v²) = 0.05
2vv₀ = 0.05 (v₀² - v²)
0.05v² + 2vv₀ - 0.05v₀² = 0
v² + 40vv₀ - v₀² = 0
quadratic formula positive answer
v = (-40v₀ + √((40v₀)² - 4(1)(v₀²))) / 2
v = (-40v₀ + √(1604v₀²)) / 2
v = (0.049968v₀) / 2
v = 0.02498439v₀
If we assume the speed of sound in air is 343 m/s
v = 8.56964... = 8.6 m/s
Approaching frequency heard is 2051 Hz
Departing frequency heard is 1951 Hz
1) velocity: 98 m/s downward
Explanation:
The marble moves by uniformly accelerated motion, with constant acceleration a=g=-9.8 m/s^2 directed towards the ground. Therefore, its velocity at time t is given by:
where
is the initial velocity
is the acceleration
is the time
Substituting t = 10 s, we find:
And the negative sign means the direction of the velocity is downward.
2) Distance covered: 490 m
The distance covered in an uniformly accelerated motion can be found with the formula:
where
is the acceleration
t is the time
Substituting t=10 s, we find
And the negative sign means the displacement is below the dropping point.