First slide

Projection Under uniform Acceleration

Question

Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true?
I. The horizontal distance travelled by the bullet is greater for the Moon.
II. The flight time is less for the bullet on the Earth.
III. The velocities of the bullets at impact are the same.

Moderate

A

III only
B

I and II only
C

I and III only
D

II and III only

Solution

The figure can be represented as follows:
The expressions are
$\begin{array}{l} h = \frac{1}{2} {gt}^{2}; t = \sqrt{\frac{2 h}{g}}; x = ut = \sqrt{\frac{2 h}{g}} u \\ or t \propto \sqrt{\frac{1}{g}}; x \propto \sqrt{\frac{1}{g}} \end{array}$
For moon, $g_{moon} = \frac{g}{6}$ , substituting in Eq. (1) and comparing, we get
$t_{Moon} = \sqrt{6} t > t_{Earth}, x_{Moon} = \sqrt{6} x > x_{Earth}$
Hence, Statements I and II both are correct. Now, v_x = u, so
$v_{y} = gt = g \sqrt{\frac{2 h}{g}} = \sqrt{2 gh}$
$or v \propto g . Since g_{Moon} = g / 6, we have v_{Moon} < v_{Earth}$ Thus, statement III is incorrect.

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