Two projectiles, one fired from earth with 5m/s and other from another planet with 3m/s trace identical trajectory. If g (earth) = 9.8 m/s², then g (planet) = ?

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Answer 1 · 2018-06-03T11:45:31

#"3.528 m/s"^2#

They trace identical trajectory. It means their range is same.

Range of a projectile is given by

#"R" = ("u"^2sin2theta)/"g"#

#"R"_1 = "R"_2#

#("u"_1^2 cancel(sin2theta))/("g"_1) = ("u"_2^2 cancel(sin2theta))/"g"_2#

#"g"_2 = "u"_2^2/"u"_1^2 × "g"_1#

#color(white)("g"_2) = "(3 m/s)"^2/"(5 m/s)"^2 × "9.8 m/s"^2#

#color(white)("g"_2) = 9/25 × "9.8 m/s"^2#

#color(white)("g"_2) = 3.528\ "m/s"^2#