A ball is projected from ground into the air. At the height of $5 \mathrm{~m}$, its velocity is $\mathbf{v}=(5 \hat{i}+5 \hat{j}) \mathrm{ms}^{-1}$. The maximum height reached by the ball is (Acceleration due to gravity $=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

• A

  $8.75 \mathrm{~m}$
• B

  $5.50 \mathrm{~m}$
• Correct answer
  C

  $6.25 \mathrm{~m}$
• D

  $10 \mathrm{~m}$

Solution

The motion of projectile is shown below
To calculate height attained we consider only vertical motion. Here, $u=5 \mathrm{~m} / \mathrm{s} ; a=-10 \mathrm{~m} / \mathrm{s}^2$ $v=0$ From $v^2-u^2=2 a s$ We have $0-5^2=2(-10) s$ $\Rightarrow \quad s=\frac{25}{20}=1.25 \mathrm{~m}$ Total maximum height reached by ball $=5+1.25=6.25 \mathrm{~m}$.

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