A rocket moves straight upward with zero initial velocity and with an acceleration $20 \mathrm{~m} / \mathrm{s}^2$. It runs out of fuel and stops accelerating at the end of $5^{\text {th }} \mathrm{sec}$. It reaches a maximum height and falls back to the earth. The speed when it hits the ground is. $\left(\right.$ Take $\left.g=10 \mathrm{~m} / \mathrm{s}^2\right)$

• A

  $100 \sqrt{2} \mathrm{~m} / \mathrm{s}$
• B

  $150 \sqrt{3} \mathrm{~m} / \mathrm{s}$
• Correct answer
  C

  $50 \sqrt{6} \mathrm{~m} / \mathrm{s}$
• D

  $75 \mathrm{~m} / \mathrm{s}$

Solution

We have $$ \begin{aligned} & \mathrm{V}_{\max }=0+20 \times 5=100 \mathrm{~m} / \mathrm{s} \\ & \text { and, }\left.\mathrm{S}\right|_{\mathrm{t}=5}=\frac{1}{2} \times 20 \times 5^2=250 \mathrm{~m} \end{aligned} $$ Speed with it will strike ground, $$ \begin{array}{lll} \mathrm{V}^2=100^2+2 \times 10 \times 250 & \\ \Rightarrow \quad V^2=10000+5000 \quad & \Rightarrow V^2=15000 \\ \Rightarrow \quad V^2=2500 \times 6 \quad \Rightarrow V=50 \sqrt{6} \mathrm{~m} / \mathrm{s} \end{array} $$

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