SATHEE: Motion in a Plane - Result Question 29

Motion in a Plane - Result Question 29

32. A projectile is fired from the surface of the earth with a velocity of $5 m s^{- 1}$ and angle $θ$ with the horizontal. Another projectile fired from another planet with a velocity of $3 m s^{- 1}$ 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 (in $m s^{- 2}$ ) given $g = 9.8 m / s^{2}$

[2014]

(a) 3.5

(b) 5.9

(d) 110.8

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Answer:

Correct Answer: 32. (a)

Solution:

(a) Trajectory is identical for both horizontal range $= \frac{u^{2} \sin 2 θ}{g}$

So that, $\frac{g_{planet}}{g_{earth}} = \frac{(u_{planet})^{2}}{(u_{earth})^{2}}$

Therefore, $g_{planet} = (\frac{3}{5})^{2} (9.8 m / s^{2})$

$= 3.5 m / s^{2}$

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Motion in a Plane - Result Question 29

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