Question

A ball falls off a table and reaches the ground in $1s$. Assuming $g=10m{s}^{-2}$. Calculate its speed on reaching the ground and the height of the table.

• A. $5m{s}^{-1}$ and $5m$
• B. $20m{s}^{-1}$ and $10m$
• C. $10m{s}^{-1}$ and $5m$
• D. $30m{s}^{-1}$ and $15m$

Answer 1

The correct option is C $10m{s}^{-1}$ and $5m$

Given,
Time taken, $t=1s$
Initial velocity, $u=0$
Acceleration due to gravity, $g=-10m{s}^{-2}$
(Upward direction is taken as positive)

Let the final speed be $v$.
From equation of motion,
$v=u+gt$
$v=(0-10\times 1)m{s}^{-1}$
$v=-10m{s}^{-1}$
Minus indicates velocity in downwards direction.

Let the height of table be $h$. Then displacement will be $-h$ as the final position is below the initial position.
From equation of motion,
$-h=ut+\frac{1}{2}g{t}^2$
$-h=0\times 1-\frac{1}{2}\times (-10)\times 1^2$
$h=5m$