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A person can jump a maximum horizontal distance (by using a 45◦ projectile angle) of 5 m on Earth. The acceleration of gravity is 9.8 m/s 2 . What would be his maximum range on the Moon, where the free-fall acceleration is g 6 ? Answer in units of m

Answer :

Answer:30 m

Explanation:

Given

Maximum Horizontal distance is 5 m on earth

launching angle[tex]=45^{\circ}[/tex]

Acceleration due to gravity on earth is [tex]9.8 m/s^2 [/tex]

Acceleration due to gravity on moon is [tex]\frac{9.8}{6}=1.63 m/s^2 [/tex]

Range of projectile is given by

[tex]R=\frac{u^2\sin 2\theta }{g}[/tex]

[tex]R_{earth}=\frac{u^2\sin 2\theta }{g}=5[/tex]----1

[tex]R_{moon}=\frac{u^2\sin 2\theta }{\frac{g}{6}}[/tex]-----2

Divide 1 & 2

[tex]\frac{5}{R_{moon}}=\frac{1}{6}[/tex]

[tex]R_{moon}=30 m[/tex]

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