A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0s . A given
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The final velocity () of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut (
) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts <em>after throwing the ball</em>.
The given parameters;
- Mass of the first astronaut, = m₁
- Mass of the second astronaut, = m₂
- Initial velocity of the first astronaut, = v₁
- Initial velocity of the second astronaut, = v₂ > v₁
- Mass of the ball, = m
- Speed of the ball, = u
- Final velocity of the first astronaut, =
- Final velocity of the second astronaut, =
The final velocity of the first astronaut relative to the second astronaut after throwing the ball is determined by applying the principle of conservation of linear momentum.
if v₂ > v₁, then , to conserve the linear momentum.
Thus, the final velocity () of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut (
) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts after throwing the ball.
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The work that is required to increase the speed to 16 knots is 14,176.47 Joules
If a catamaran with a mass of 5.44×10^3 kg is moving at 12 knots, hence;
5.44×10^3 kg = 12 knots
For an increased speed to 16knots, we will have:
x = 16knots
Divide both expressions
To get the required work done, we will divide the mass by the speed of one knot to have:
Hence the work that is required to increase the speed to 16 knots is 14,176.47 Joules
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