Question

A ball is thrown vertically upwards with a velocity of $10\text{m/s}$. It returns to the ground with velocity of $9\text{m/s}$. If $g=9.8{\text{m/s}}^2$, then the maximum height attained by the ball is nearly (assume air resistance to be uniform)

• A. $5.1\text{m}$
• B. $4.1\text{m}$
• C. $4.61\text{m}$
• D. $5.0\text{m}$

Answer 1

The correct option is C $4.61\text{m}$

Total energy loss due to air friction $=K_i-K_f=\frac{1}{2}m(100-81)$
$=\frac{19}{2}m(m=\text{mass})$
Half of the loss will be in upward journey.
Hence, $mgh+\frac{1}{2}\left(\frac{19}{2}m\right)=K_i=\frac{1}{2}m\left(100\right)=50m$
$\therefore h=4.61\text{m}$