A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$).

• A

  $0.6 \mathrm{~ms}^{-1}$
• B

  $0.8 \mathrm{~ms}^{-1}$
• C

  $0.2 \mathrm{~ms}^{-1}$
• Correct answer
  D

  $0.4 \mathrm{~ms}^{-1}$

Solution

Time of flight, $\begin{aligned} & T=\sqrt{\frac{2 H}{g}}=\sqrt{\frac{2 \times 500}{10}}=10 \mathrm{~s} \\ & \therefore R=u . T \Rightarrow u=\frac{400}{10}=40 \mathrm{~m} / \mathrm{s} \end{aligned}$ $\therefore$ Recoil velocity of gun, $\therefore \quad \mathrm{V}=\left(\frac{\mathrm{m}}{\mathrm{M}}\right) \mathrm{u}=\frac{1 \times 40}{100}=0.4 \mathrm{~m} / \mathrm{s}$

Hence, the correct answer is option: 'D'.