Question

A tank moves uniformly along x-axis. It fires a shot from origin at an angle of 30⁰ with horizontal while moving along positive x-axis and the second shot is also fired similarly except that the tank moves along negative x-axis. If the respective range of the shot are 250 m and 210m along x-axis, then the initial velocity values are

• A. 12 m/s and 21 m/s
• B. 53 m/s and 49 m/s
• C. 95 m/s and 58m/s
• D. 79 m/s and 19 m/s

Answer 1

Answer: (B)

53 m/s and 49 m/s

Answer 2

Let u be the velocity of projectile w.r.t. tank’s velocity v, then for x axis ,

U_x = u cos 30⁰ + v

U_y = u sin 30⁰

and T = 2usin30/g

Range, R₁ = U_xT

= 2usin30⁰/g (u cos 30⁰ + v)

for y axis,

U'_x = u cos 30⁰ – v

and U'_y = u sin 30⁰

T = 2usin30⁰/g

Range, R₂ = TU'_x

= 2usin 30⁰/g (u cos 30⁰ - v)

Then, R₁ + R₂ = 4u²/g (sin 30s cos 30)

R₁ – R₂ = 4u/g v sin30

Eliminating u, we get

v² = $\frac{g}{4\tan 30} - \frac{\left( R_{1} - R_{2} \right)^{2}}{\left( R_{1} + R_{2} \right)}$

= $\frac{10}{4\tan 30}\frac{(250 - 200)^{2}}{(250 + 200)}$= 24 m²s^-2

or v = 4.9ms^-1