The maximum range of a gun of horizontal terrain is 16 km. If g = 10 ms - 2, then muzzle velocity of a shell must be

Question

The maximum range of a gun of horizontal terrain is 16 km. If g = 10 ms - 2, then muzzle velocity of a shell must be (A) 160 ms - 1 (B) 200 √ 2 ms - 1 (C) 400 ms - 1 (D)  800 ms - 1

Tardigrade Admin · Accepted Answer

Horizontal range R=(u2 sin 2 θ/g) For maximum horizontal range θ=45° or Rm=(u2/g) where u be muzzle velocity of a shell ∴ (1600 m )=(u2/(10 ms -2)2) or u=400 ms -1.

Q. The maximum range of a gun of horizontal terrain is $16 km$ . If g = $10 m s^{- 2}$ , then muzzle velocity of a shell must be

$160 m s^{- 1}$

$2002 m s^{- 1}$

$400 m s^{- 1}$

$800 m s^{- 1}$

Horizontal range $R = \frac{u ^{2} s i n 2 θ}{g}$
For maximum horizontal range $θ = 4 5^{\circ}$
or $R_{m} = \frac{u ^{2}}{g}$ where $u$ be muzzle velocity of a shell
$∴ (1600 m) = \frac{u ^{2}}{( 10 m s ^{- 2} ) ^{2}}$
or $u = 400 m s^{- 1}$ .

Q. The maximum range of a gun of horizontal terrain is 16km. If g = 10ms−2, then muzzle velocity of a shell must be

160ms−1

2002​ms−1

400ms−1

800ms−1