Question

A body,thrown vertically upwards with an initial velocity $u$, reaches maximum height in $6$ seconds. The ratio of the distance travelled by body in the first second and the eleventh second is:

• A. $1:1$
• B. $11:9$
• C. $1:2$
• D. $9:11$

Answer 1

The correct option is B $11:9$

The body reaches maximum height in 6 seconds and the velocity will be zero at maximum height.
$v=u-gt$
$\Rightarrow 0=u-\left(9.81\right)\left(6\right)$
$\Rightarrow u=58.86m/s$

Distance traveled in the first second is:
$s_1=58.86\left(1\right)-0.5\left(9.81\right)\left(1^2\right)=53.955m$
Distance traveled in the eleventh second is the distance traveled in the 5th second during the descent, i.e.,

$s_{11}=0.5\left(9.81\right)(5^2-4^2)=44.145m$
The ratio is:

$53.955:44.145=11:9$