Kinematics 5 Question 6
8. Two guns $A$ and $B$ can fire bullets at speeds $1 km / s$ and $2 km / s$, respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets on the ground fired by the two guns is
(Main 2019, 10 Jan I)
(a) $1: 4$
(b) $1: 16$
(c) $1: 8$
(d) $1: 2$
Show Answer
Answer:
Correct Answer: 8. (b)
Solution:
- Bullets from guns can reach upto a distance of maximum range which occurs when projection is made at angle of $45^{\circ}$. Maximum range for gun
$$ A=R _1=\frac{u _1^{2}}{g} $$
Maximum range for gun
$$ B=R _2=\frac{u _2^{2}}{g} $$
So, ratio of covered areas
$$ =\frac{\pi\left(R _1\right)^{2}}{\pi\left(R _2\right)^{2}}=\frac{\pi \cdot u _1^{4} / g^{2}}{\pi \cdot u _2^{4} / g^{2}}=\frac{u _1^{4}}{u _2^{4}} $$
Here, $u _1=1 km / s$ and $u _2=2 km / s$
So, ratio of areas $=\frac{1^{4}}{2^{4}}=\frac{1}{16}=1: 16$
