Question

Identical guns fire bullets horizontally at the same speed from the same height above level planes. One on the earth and one on the moon (knowing that the acceleration due to gravity in moos is one-sixth that of the earth). Which of the following statements is incorrect?
A. The horizontal distance cover by the bullet is greater for the moon.
B. The flight time is less for bullets on earth.
C. The velocity of the bullet at impact is the same.
D. The velocity of the bullet at impact is greater for the earth.

Answer 1

Acceleration due to gravity is the acceleration gained by a body due to the attractive force known as gravitational force. Gravitational force tries to pull every object in the universe towards it. Acceleration due to gravity is denoted by ‘g’ and its value is constant on earth but the value changes over different places in the space.

Complete step-by-step answer:
As we already know that the acceleration due to gravity is $\dfrac{1}{6}$ times the value of g on earth. The constant value of g on earth in $9.8m{{s}^{-2}}$.
As per the question, a bullet is fired at the same speed and height above the reference level on earth and moon.
The horizontal distance covered by the bullet at a certain height from the ground is inversely proportional to the acceleration due to acceleration due to gravity acting on the body.
${{x}_{h}}\propto \dfrac{1}{g}$
As the value of g on the moon is less than that on earth. Therefore the horizontal distance covered by the bullet on the moon will be greater.
The time of flight of a projectile is given by
$\begin{aligned} & t=\dfrac{2v\sin \theta }{a} \\\ & \Rightarrow t\propto \dfrac{1}{a} \\\ \end{aligned}$
Thus, the time of flight on earth will be less.

The velocity of the bullet is dependent on the acceleration due to gravity acting on the body. The velocity of the bullet can be given as,
$v=({{v}_{\circ }}\sin {{\theta }_{\circ }})-gt$
So the velocity of the object will be different for both the places (earth and moon).
And from the same formula of velocity, we can say that the velocity of the bullet is directly proportional to the acceleration due to gravity on earth. Thus greater the value of g higher will be the velocity of the object.
$v\propto g$
So the velocity of the bullet will be greater on the earth.
From the above discussion we can conclude that only one statement in the options is incorrect, that is Option C. and this is the option for which it is asked in the question.

So, the correct answer is “Option C”.

Note: When a bullet is fired at a certain height above the ground level the bullet undergoes in projectile motion. The projective motion of the body is highly dependent on the acceleration due to gravity acting on the body. As the value of g changes automatically we can observe the changes in the motion of the body.