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Sagot :
Answer:
The person can jump 48 m on the Moon
Explanation:
The question parameters are;
The maximum long jump distance of a person on Earth, [tex]R_{max}[/tex] = 3 m
The acceleration due to gravity on the Moon = 1 ÷ 16 of that on Earth
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, [tex]R_{max}[/tex], of a projectile motion is found by using the following formula
[tex]R_{max} = \dfrac{u^2}{g}[/tex]
Where;
g = The acceleration due to gravity = 9.8 m/s²
Therefore, we have;
[tex]R_{max} = 3 \, m = \dfrac{u^2}{9.8 \, m/s^2 }[/tex]
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, [tex]g_{Moon}[/tex] = 1/16 × g
∴ [tex]g_{Moon}[/tex] = 1/16 × g = 1/16 × 9.8 m/s² ≈ 0.6125 m/s²
[tex]R_{max \ Moon} = \dfrac{u^2}{g_{Moon}} = \dfrac{29.4 \ m^2/s^2}{0.6125 \, m/s^2 } \approx 48 \, m[/tex]
The maximum distance the person can jump on the Moon with the same velocity which was used on Earth is [tex]R_{max \ Moon}[/tex] ≈ 48 m
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