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Projectile Time, Height and Range

A projectile ...

Question

A projectile is fired from the surface of the earth with a velocity of $5 {ms}^{- 1}$ and 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 (in ${ms}^{- 2}$ ) is
(Given $g = 9.8 {ms}^{- 2}$ )

A

3.5

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B

5.9

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C

16.3

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D

110.8

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Solution

The correct option is A $3.5$
If both the trajectories are identical, then
$H_{e} = H_{p}$ ( $H$ is the maximum height of a projectile)
$\Rightarrow \frac{5^{2} {sin}^{2} θ}{2 g_{e}} = \frac{3^{2} {sin}^{2} θ}{2 g_{p}}$ ( $θ$ is same in both the case)
$\Rightarrow g_{p} = \frac{9}{25} g_{e}$
$= \frac{9}{25} \times 9.8 = 3.52 {m/s}^{2}$
Hence, the correct answer is option (A).

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