How Does Gravity Affect Projectile Distance on the Moon Compared to Earth?

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SUMMARY

The discussion focuses on calculating the horizontal distance a stone travels when thrown on the Moon compared to Earth. Using the formula for range, RE = u²sin²θ/g, where g is the acceleration due to gravity, the user initially misapplies the range formula. After corrections, it is established that the correct horizontal distance on the Moon, RM, is 0.82 times the Earth's radius, leading to the conclusion that the correct answer is option c) 3.06RE.

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Homework Statement



A stone is thrown with an initial velocity 5m/s such that it covers maximum possible horizontal distance RE on the surface of the Earth. The same stone is thrown with same initial velocity by a person standing on the moon, making an angle of 150 with the surface. given that acceleration due to gravity on Earth's surface is g=9.8m/s2 and that on moon's surface is gm=1.6m/s2, the horizontal distnace it covers on the moon is
a) 0.326RE
b) 0.326/RE
c) 3.06RE
d) -0.629RE

Homework Equations



RE=u2sin2θ/g

The Attempt at a Solution



RE=u2/2ge
so u2=2geRE
Now, RM=u2sin215/gm
substitute u2 in RM
therefore RM=2geRE(0.067)/1.6
after solving I get RM=RE(0.82)
I know I'm missing the mark due to some stupid mistake somewhere, could you please point it out?
 
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Got it. I got the range formula wrong. the answer is c)
 
nice save :)
 

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