<u>Yes. The speed of a rocket can exceed the exhaust speed of the fuel.</u>
How this is explained?
- The thrust of the rocket does not depend on the relative speed of the gases or the relative speed of the rocket.
- It depends on conservation of momentum.
What is conservation of momentum?
- Conservation of momentum, general law of physics according to which the quantity called momentum that characterizes motion never changes in an isolated collection of objects; that is, the total momentum of a system remains constant.
- Momentum is equal to the mass of an object multiplied by its velocity and is equivalent to the force required to bring the object to a stop in a unit length of time.
- For any array of several objects, the total momentum is the sum of the individual momenta.
- There is a peculiarity, however, in that momentum is a vector, involving both the direction and the magnitude of motion, so that the momenta of objects going in opposite directions can cancel to yield an overall sum of zero.
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The formula for the acceleration due to gravity is:
a = Gm/r²
where
G is the universal gravitational constant = 6.6726 x 10⁻¹¹ N-m²/kg²
m is the mass of planet
r is the radius of planet
So, if they have the same a:
m₁/r₁² = m₂/r₂²
So, if m₁ = m and r₂ = 2r₁,
m/r₁² = m₂/(2r₁)²
m₂ = 4m
<em>Thus, the answer is D.</em>
Answer: The wave can flip upside down.
Reflection is the bending of a wave when it cannot pass through. For example, plain mirrors which are flat, a ray of light hits the mirror and is reflected from the mirror since it cannot pass through
When reflection occurs the speed and frequency of the wave does not change but the wave is flipped upside down.
The speed does not change because speed is affected by the change in medium the frequency also remains the same since the energy of the wave does not change.
Kinetic energy of pieces A and B are 2724 Joule and 5176 Joule respectively.
<h3>What is the relation between the masses of A and B?</h3>
Mass of piece B = Mb
- Velocities of pieces A and B are Va and Vb respectively.
- As per conservation of momentum,
Ma×Va = Mb×Vb
So, 1.9Mb × Va = Mb×Vb
=> 1.9Va = Vb
<h3>What are the kinetic energy of piece A and B?</h3>
- Expression of kinetic energy of piece A = 1/2 × Ma × Va²
- Kinetic energy of piece B = 1/2 × Mb × Vb²
- Total kinetic energy= 7900J
=>1/2 × Ma × Va² + 1/2 × Mb × Vb² = 7900
=> 1/2 × Ma × Va² + 1/2 × (Ma/1.9) × (1.9Va)² = 7900
=> 1/2 × Ma × Va² ×(1+1.9) = 7900 j
=> 1/2 × Ma × Va² = 7900/2.9 = 2724 Joule
- Kinetic energy of piece B = 7900 - 2724 = 5176 Joule
Thus, we can conclude that the kinetic energy of piece A and B are 2724 Joule and 5176 Joule respectively.
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