Question

A ball is thrown vertically upwards with an initial velocity $u$ reaches maximum height in $5\, \sec$. The ratio of distance travelled by the ball in the second and seventh second is: (Assume $g =10\, m / s ^{2}$)

• A. $8: 19$
• B. $16: 29$
• C. $16: 49$
• D. $8: 49$
• E. None of the above

Answer 1

Answer: (E)

When ball is at maximum height, its velocity is zero.
From first equation of motion,
$v=u-g t$
$\Rightarrow 0=u-10 \times 5$
$\Rightarrow u=50\, m / s$
Distance travelled in $n$th second,
$s_{n}=u+\frac{a}{2}(2 n-1)$
Distance travelled in 2 nd second is given as
$s_{2}=50-\frac{10}{2}(4-1)=50-15=35\, m$
Distance travelled in $7th$ second is equal to distance travelled in $2nd$ second from highest point to vertically downward direction.
$s_{7}=s_{2}=0+\frac{10}{2}(2 \times 2-1)=15\, m$
$\therefore \frac{s_{2}}{s_{7}}=\frac{s_{2}}{s_{2}}=\frac{35}{15}=\frac{7}{3}$
or $7: 23$