A projectile is fired from the surface of the earth with a velocity of $$5$$ $$ms-1and$$ angle θ with the horizontal. Another projectile fired from another planet with a velocity of $$3$$ $$ms-1$$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (ms-2) is $$(Given$$ g $$=$$ $$ms-2$$

Question

A projectile is fired from the surface of the earth with a velocity of $$5$$ $$ms-1and$$ angle θ  with the horizontal. Another projectile fired from another planet with a velocity of $$3$$ $$ms-1$$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (ms-2) is $$(Given$$  g $$=$$ $$ms-2$$

Infinity Learn · Accepted Answer

The equation of trajectory is $$y=xtan$$⁡θ−$$gx22u2cos2$$⁡θwhere θ is the angle of projection and u is the velocity with which projectile is projected. For equal trajectories for same angles of projection,  $$gu2=$$ constant As per question $$9.852=g$$′$$32where$$ g' is acceleration due to the gravity on the planet. g′$$=9.8$$×$$925=3.5ms$$−$$2$$

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