JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Kinematics

Two guns A and B can fire bullets at speed

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 fired by the two guns, on the ground is:

(A) $1 : 16$ ✓ Correct
(B) $1 : 2$
(C) $1 : 4$
(D) $1 : 8$

Answer: (A)

Solution

A gun firing in all directions covers a circle whose radius is the maximum range

R = \frac{v ^{2}}{g}

, so the ground area reached is

A = π R^{2} = π \frac{v ^{4}}{g ^{2}}

, scaling as the fourth power of the muzzle speed. Doubling the speed therefore multiplies the area by

2^{4} = 16

, so the areas for the

1

km/s and

2

km/s guns stand in the ratio

1 : 16

. That strong fourth-power dependence is why a small edge in launch speed becomes a large edge in ground covered.

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Kinematics →

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Kinematics

Solution

More JEE Main questions on Kinematics