A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of ball thrown per minute is (take g = 10m/s²)

The correct option is 60.

Step-by-step Explanation:

1. Identify the given information:
Maximum height reached by each ball, $H=5\text{m}$
Acceleration due to gravity, $g=10{\text{m/s}}^2$
The next ball is thrown when the previous ball reaches its maximum height. This means the time interval between two consecutive throws is equal to the time taken by a ball to reach its maximum height.

2. Calculate the time taken to reach the maximum height ($t$):
When a ball reaches its maximum height, its final velocity ($v$) is $0\text{m/s}$.
Using the equation of motion:

$v^2=u^2-2gH$

$0=u^2-2gH$

$u^2=2gH$

Substituting the given values:

$u^2=2\times 10\times 5=100$

$u=10\text{m/s}$

Now, use another equation of motion to find the time ($t$) to reach maximum height:

$v=u-gt$

$0=10-10t$

$10t=10$

$t=1\text{second}$

So, one ball is thrown every 1 second.

3. Calculate the number of balls thrown per minute:
Since 1 ball is thrown every 1 second, and there are 60 seconds in one minute:

$\text{Number of balls thrown per minute}=\frac{60\text{seconds}}{1\text{second/ball}}=60$

Thus, 60 balls are thrown per minute.