Solving Projectile Motion: What Step Does Ball Hit First?

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SUMMARY

The discussion focuses on calculating which step a ball will hit first after rolling horizontally off a stairway at a speed of 1.52 m/s. The steps are 1.52 cm high and 20.3 cm wide. The key formula derived is T = √(2gh)/g for the time of flight, where h is the height of a step and n is the number of steps passed. The range of the ball is determined by the equation nw = v/g x √(2gh), where w is the width of the steps, leading to the conclusion that n should be rounded up to find the number of steps the ball descends.

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A ball rolls horizontally off the top of a stairway with a speed of 1.52m/s. The steps are 1.52 cm high, and 20.3 cm wide, which step does the ball hit first.

I don't really know where to start, I kept trying to use the formulas..but I would always end up with two unknowns.

Can anyone point me in the right direction?
 
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suspenc3 said:
A ball rolls horizontally off the top of a stairway with a speed of 1.52m/s. The steps are 1.52 cm high, and 20.3 cm wide, which step does the ball hit first.
I don't really know where to start, I kept trying to use the formulas..but I would always end up with two unknowns.
Can anyone point me in the right direction?
The range of the ball is vT, where v = 1.52m/s and T is the duration: T = ROOT(2gnh)/g where h is the height of a step and n is the number of them passed. The range is also the sum of the widths of the steps passed, so:

nw = v/g x ROOT(2gnh)

where w = 20.3 x 10^-2.

Rearrange and solve for n, rounding down.
 
Sorry, I was counting steps 'across' when I said round down. You should round up for how many steps down the ball goes. Makes more sense.
 

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