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Artemon [7]
3 years ago
7

An train car of total mass of 13000 kg is pulling into a station and slowing down with an acceleration of -4.56 m/s^2. Before th

e train pulls into the station, a group of 7 stowaway jump off the train. Each stowaway has a mass of 66 kg. If the braking force on the train remains the same, what will be the acceleration of the train once the stowaways jump out of the train?

Physics
1 answer:
lys-0071 [83]3 years ago
4 0
<h3>Answer:</h3>

-4.73 m/s²

<h3>Explanation:</h3>

Each jumper represents about 1/2 of 1% of the mass of the train, so together they total about 3.5% of the mass of the train. If the mass decreases by 3.5% and the braking force remains the same, the acceleration (magnitude) will increase by about 3.5%.

The acceleration will be about 0.17 m/s² more (in magnitude) than it was, or about -4.73 m/s².

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The maximum long jump distance of a person on Earth, R_{max} = 3 m

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The distance the person can jump on the Moon is given as follows;

A person performing a jump across an horizontal distance on Earth (under gravitational force) follows the path of the motion of a projectile

The horizontal range, R_{max}, of a projectile motion is found by using the following formula

R_{max} = \dfrac{u^2}{g}

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Therefore, we have;

R_{max} = 3 \, m = \dfrac{u^2}{9.8 \, m/s^2 }

u² = 3 m × 9.8 m/s² = 29.4 m²/s²

Therefore, on the Moon, we have;

The acceleration due to gravity on the Moon, g_{Moon} = 1/16 × g

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R_{max \ Moon} = \dfrac{u^2}{g_{Moon}}   = \dfrac{29.4 \ m^2/s^2}{0.6125 \, m/s^2 } \approx 48 \, m

The maximum distance the person can jump on the Moon with the same velocity which was used on Earth is R_{max \ Moon} ≈ 48 m

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