Kinematics Question 620
Question: A projectile is fired from the surface of the earth with a velocity of 5 $ m{{s}^{-1}} $ and angle $ \theta $ 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 it’s (in $ \text{m}{{\text{s}}^{-2}} $ ) given $ \text{g = 9}\text{.8 m/}{{\text{s}}^{\text{2}}} $
Options:
A) 3.5
B)5.9
C) 163
D)110.8
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Horizontal range = $ \frac{{u^{2}}\sin 2\theta }{g}\text{ so g}\propto {u^{2}} $
$ \text{or }\frac{{{\text{g}} _{\text{planet}}}}{{{\text{g}} _{\text{earth}}}}=\frac{{{( {{\text{u}} _{\text{planet}}} )}^{2}}}{{{( {{\text{u}} _{\text{earth}}} )}^{2}}} $
$ \text{Therefore }{{\text{g}} _{\text{planet}}}={{( \frac{3}{5} )}^{2}}( 9.8\text{ m/}{s^{2}} ) $
$ =3.5\text{ m/}{s^{2}} $
