A marble is thrown over the horizontal surface on the top of some stairs, and it
leaves the top of the stairs with horizontal speed of 3 m/s. Each step goes down
18 cm and is 30 cm wide. On which step will the marble land?
i need your help?
2019-02-20 3:59 pm
回答 (2)
2019-02-20 7:34 pm
Take g = 9.81
Assume that the marble will land on the nth step.
Then, the vertical displacement is 0.18n m, and the horizontal displacement is less than 0.3n m.
Consider the vertical motion:
Time taken, t = √(2h/g) = √(2×0.18n/9.81) s = 0.192√n s
Horizontal displacement < 0.3n m
(Horizontal velocity) × time < 0.3n m
(3 m/s) × (0.192√n s) < 0.3 n m
0.576√n < 0.3n
n/√n > 0.576/0.3
√n > 1.92
n > 1.92²
n > 3.69
As n is an integer, n = 4
Hence, the marble will land on the 4th step.
Assume that the marble will land on the nth step.
Then, the vertical displacement is 0.18n m, and the horizontal displacement is less than 0.3n m.
Consider the vertical motion:
Time taken, t = √(2h/g) = √(2×0.18n/9.81) s = 0.192√n s
Horizontal displacement < 0.3n m
(Horizontal velocity) × time < 0.3n m
(3 m/s) × (0.192√n s) < 0.3 n m
0.576√n < 0.3n
n/√n > 0.576/0.3
√n > 1.92
n > 1.92²
n > 3.69
As n is an integer, n = 4
Hence, the marble will land on the 4th step.
2019-02-20 4:21 pm
If t = sqrt( 2h/g) = sqrt( 2*n*0.18/9.8) and s =3t
I set it as an input into a spreadsheet
seeking the first value of n where s ( the horizontal distance moved ) is less than n * 0.3 ( the width of the steps to that point. )
This was reached on the fourth step. So the marble lands somewhere on this step.
I set it as an input into a spreadsheet
seeking the first value of n where s ( the horizontal distance moved ) is less than n * 0.3 ( the width of the steps to that point. )
This was reached on the fourth step. So the marble lands somewhere on this step.
收錄日期: 2021-04-24 07:28:49
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