Question

25. A projectile is fired from the surface of the
earth with a velocity of 5 m s' and angle e
with the horizontal. Another projectile fired from
another planet with a velocity of 3 m s' 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) is (Given g = 9.8 m s-2)
(a) 3.5 (b) 5.9 (c) 16.3 (d) 110.8 (2014)​

Answer 1

Answer - option (b) 5.9 will be correct ans.

Explanation-

in both case trajectory is same. so this imply their displacement/ trajectory along y axis will also be same.

for the 1st case-

$y = 5t - 1 \div 2g {t}^{2}$

in 2 nd case -

$y = 3t - 1 \div 2a {t}^{2}$

as y axis displacement is same

$5t - 1 \div 2g {t }^{2} = 3t - 1 \div 2a {t}^{2}$

if t=1 then

5 - 4.9 = 3 -a/2

a/2 = 3 - 0.1

a/2 = 2.9

a= 2.9 × 2 = 5.8 which is app. 5.9

hope it helps ☺