Question

A ball is thrown into a lake from a tower $20\text{m}$ above the water surface. The ball hits the water after $1\text{sec}$ with a velocity $v$ and then sinks to the bottom of the lake. It comes to rest at the bottom of the lake $6\text{sec}$ after it was thrown. Find the acceleration of the ball inside the lake and the depth of the lake.

• A. $5m/s^2,62.5m$
• B. $-5m/s^2,75m$
• C. $-5m/s^2,62.5m$
• D. $$ 5m/s^2,75m$$

Answer 1

The correct option is C $-5m/s^2,62.5m$

Let $u$ be the velocity with which the ball is thrown.
Using 2nd equation of motion, (taking downward +ve)
$h=ut+\frac{1}{2}g{t}^2\Rightarrow 20=u\times 1+\frac{1}{2}\times 10\times 1^2\Rightarrow u=15m/s$

The velocity of the ball as it is about to touch the surface of the water, $v=u+at\Rightarrow v=15+10\times 1\Rightarrow v=25m/s$

The ball takes $(6-1)=5\text{sec}$ to reach from the surface to the bottom of the lake.

For the ball's motion inside water, $u=25m/s,v=0\mathrm{and}t=5\mathrm{seconds}$
$v=u+at\Rightarrow 0=25+a\times 5\Rightarrow a=-5m/s^2$
The negative sign of acceleration shows that the ball slows down while traveling inside the water of the lake.

The depth of the lake, $s=ut+\frac{1}{2}a{t}^2\Rightarrow s=25\times 5-\frac{1}{2}\times 5\times 5^2\Rightarrow s=(125-62.5)m\Rightarrow s=62.5m$