Balls Thrown Up

Classical Mechanics Level 1

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 maximum height. If the maximum height reached by each ball is 45 meters, then find the number of balls thrown up in a minute.

Assume that $g = -9.8$ m/s $^2$ , and ignore factors like wind resistance.

10 20 40 60

2 solutions

Abc Xyz
Apr 7, 2016

Maximum Height reached by an object is given = $\frac{u^2}{2g}$ **

where $g = 10 m/s^2$ and Height = 45 metres.

So by simple calculations,

u = $\sqrt{900}$ = 30 m/s

Time to reach maximum height is given = $\frac{u}{g}$ **

Therefore time taken is $\frac{30}{10}$ = 3 seconds.

One minute is 60 seconds.

So we need $\frac{60}{3}$ = 20 .........since balls are thrown up in every 3 seconds for a duration of 60 seconds.

Thus the answer is $\boxed{20}$

** These are formulae.........If u want to know their proofs then u can ask me.......

The proofs? No I know about them . But it's good that u got it correct . :D

Abhiram Rao - 5 years, 2 months ago

:> Happy to know.

abc xyz - 5 years, 2 months ago

You forgot the ball that's thrown at 60 s. It will make 21 balls within the minute.

Leif Hoving - 5 years ago

But it doesn't reach the maximum height in a minute so , it should be 20 right?

Abhiram Rao - 5 years ago

@Abhiram Rao – Ball(20) has reached 45 meters at 60 seconds. At that moment I have the right to throw ball(21). Both ends 0 and 60 belong to the closed interval. If You instead use g = 9.81 m/ss then You get rid of this 'problem' because it will take ~ 3.03 seconds to reach 45 meters.

Leif Hoving - 5 years ago

@Leif Hoving – Oh yeah..Thanks for informing. I have edited the question. :)

Abhiram Rao - 5 years ago

Wow.....-9.8m/s^2 gives me 3.03seconds...by the way, good question!

Bad SQ - 4 years, 7 months ago

Abhiram Rao
Mar 28, 2016

As the maximum height reached is 45 meters , the initial velocity of the ball will be square root of 2 . g . maximum height = 30 m/s.
So , the time taken to reach the maximum height = u/g = 30/10 = 3 seconds.
The no. of balls which can be thrown up in a minute = 60/3 = 20

Balls Thrown Up

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