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Old 10-20-2010, 11:30 PM   #1
Wyrm
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Default Grade 12 Physics Problems


I would appreciate it if someone could help me with the following problem.

A ball is thrown at an angle of 45 degrees at a speed of 40m/s. Each time it bounces, it loses 75% of its speed. How far does it travel before it stops?

What I don't understand is that because it only loses 75% of its speed, doesn't that mean it never stops?

If someone could explain a solution to me, I'd be grateful.
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Old 10-21-2010, 02:31 AM   #2
-Cirno
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Default Re: Grade 12 Physics Problems

^
geometric sequence...
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Old 10-21-2010, 02:32 AM   #3
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Default Re: Grade 12 Physics Problems

and yeah, that question seems to lack more info...
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Old 10-21-2010, 03:55 PM   #4
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Default Re: Grade 12 Physics Problems

The each time it bounces loses 75% of its speed is a data, depend on the floor material and the ball material.

We decompose the speed in 2 speeds, one forward (->) and one up (/|).

Each of these speeds is sqrt (2) * 20 (do the math).

Now the ball accelerates downwards (|/) at 10m/s*s.
So it takes sqrt (2) * 20/10 = sqrt (2) * 2 seconds to stop going up and start going down.
In that time it moved sqrt (2) * 2 * sqrt (2) * 20 = 80m. (sqrt (2) * 2 = time, sqrt (2) * 20 = speed).
Since it has constant acceleration it describes a parabola. We know the vertex is between both roots, so that means it hits the ground again at 160m.

Now the next time, the speed will be 10m/s and the starting angle will be the same.

This means it moves 160m * 1/4, or 40m. We can keep on like this forever since it will never stop, but we do realize that it moves always slower.

So it moves

160m * (1+1/4+1/4/4+1/4/4/4.................) = 160 * (1+1/4+1/16+1/64........)

Now some math.

1 + 1/x + 1/x2 + 1/x3 + 1/x4.... 1/xn + 1/x n+1) = 1 + 1/x-1. (this applies for all x > 1)

So 160m * (1+1/4+1/4/4+1/4/4/4......................) = 160 * (1+1/4+1/16+1/64..........) = 160 * (1+1/3) = 160m * 4/3 = 640m/3.

The ball moves 640m/3. Though it actually never stops.
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Old 10-21-2010, 10:11 PM   #5
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Default Re: Grade 12 Physics Problems

Thanks.
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Old 10-21-2010, 10:15 PM   #6
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Default Re: Grade 12 Physics Problems

True, that is the closest answer, IMO, the question itself is wrong since the ball would literally never stop on a closed system (and we didn't deal with friction either)
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Old 10-21-2010, 10:29 PM   #7
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Default Re: Grade 12 Physics Problems

Reminds me of one of my old physics problems, although I don't remember exactly how it was formulated.
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Old 10-23-2010, 06:11 AM   #8
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Default Re: Grade 12 Physics Problems

Fuck, shamanics answered it again. Well he is 200% right. My all labour solving on my note-book went in vain.
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