Question

A juggler maintains four balls in the air with air with throwing speed $20$ m/s upwards in regular time intervals. When one ball is about to leave his hand the height of balls in air from the ground will be:

• A. $60m,80m,60m,0m$
• B. $30m,40m,30m,0m$
• C. $15m,20m,15m,0m$
• D. $10m,20m,10m,0m$

Answer 1

The correct option is C $15m,20m,15m,0m$

Initial velocity $u=20m/s$

Final velocity $v=0m/s$

Acceleration $a=-10m/s^2$

Now, the time by ball reach its maximum height

From equation of motion

$v=u+at$

$0=20-10t$

$t=2s$

So, the time taken by the same ball to return to the hands of the juggler is

$=\frac{2u}{g}$

$=\frac{2\times 20}{10}$

$=4s$

So, he is throwing the balls after 1 sec each,

Let at some instant he throws ball number 4.

Now, Before 1 s of throwing it, he throws ball 3.

So, the height of ball 3 is

$h_3=20\times 1-\frac{1}{2}\times 10\times {\left(1\right)}^2$

$h_3=15m$

Before 2s, he throws ball 2, so the height of ball 2 is

$h_2=20\times 2-\frac{1}{2}\times 10\times 4$

$h_2=20m$

Before 3s, he throws ball 1, so the height of ball 1 is

$h_1=20\times 3-\frac{1}{2}\times 10\times 3\times 3$

$h_3=15m$

Hence, the height of balls in air from the ground will be $15m$, $20m$, $15m$ and $0m$