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 $g=10m/s^2$)

• 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,
$v=u-gt$
$\Rightarrow 0=u-10\times 5$
$\Rightarrow u=50m/s$
Distance travelled in $n$th second,
$s_n=u+\frac{a}{2}(2n-1)$
Distance travelled in 2 nd second is given as
$s_2=50-\frac{10}{2}(4-1)=50-15=35m$
Distance travelled in $7th$ second is equal to distance travelled in $2nd$ second from highest point to vertically downward direction.
$s_7=s_2=0+\frac{10}{2}(2\times 2-1)=15m$
$\therefore \frac{s_2}{s_7}=\frac{s_2}{s_2}=\frac{35}{15}=\frac{7}{3}$
or $7:23$